Most Asked Aptitude Questions Answers with Explanation For MNC and Competitive Exams

1. Twice the speed of a boat downstream is equal to thrice the speed upstream. The ratio of its speed in still water to the speed of current is

A. 1 : 5

B. 1 : 3

C. 5 : 1

D. 2 : 3

Explanation :

Let the boat speed in still water be b.

Let the stream speed be x.

2(b+ x) = 3(b-x)

5x=b

b/x=5/1

2. A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed with that chemical so that after selling the mixture at Rs. 20/litre he may get a profit of 25%?

A. 13 : 16

B. 12 : 15

C. 9 : 16

D. 19 : 22

Explanation :

This can be solved using alligation.

What is required at the end of mixing is a price of 20/1.25 = 16.

So the alligation would look like this –

Water/0 Mixture/16 Chemical/25

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Hence the ratio would be (25 – 16) : 16 = 9 : 16

Hence required ratio of Water : Chemical is 9:16.

3. The difference between the simple interest and compound interest on a certain sum of money for 2 years at 15% p. a. is Rs. 45. Find the sum.

A. Rs. 2700

B. Rs. 2500

C. Rs. 2000

D. None of these

Explanation :

Since we know that the interest rate is 0.15, and knowing that the difference between two years of compound interest is nothing but interest on interest, we can find the first year’s interest as –

45/0.15 = 300.

Now if the interest is 300 at the end of one year, then the principal is 300 / 0.15 = 2,000

4. How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively, and the sum of terms is 40?

A. 15

B. 10

C. 5

D. 20

Explanation :

Now the common difference of this AP is 16/4 = 4.

The sum of an AP is n/2 {2a + (n – 1)d}

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Substituting we get, 40 = n/2 {2×-14 + (n – 1)4}

The best way to solve this is by plugging options. Put in n = 10 and get the RHS as 40.

5. In a class, 50 students play cricket, 20 students play football and 10 play both cricket and football. How many play at least one of these two games?

A. 10

B. 80

C. 50

D. 60

Explanation :

The required answer is 50 + 20 – 10 = 60.

6. A bottle is full of Dettol. One-third of it is taken out and then an equal amount of water is poured into the bottle to fill it. This operation is done four times. Find the final ratio of dettol and water in the bottle.

A. 13 : 55

B. 20 : 74

C. 16 : 65

D. 10 : 48

Explanation :

As in denominator we have to take 1/3 four times so, we start by assuming 81 ml of dettol in the bottle. After the first iteration you will be left with

2/3 × 81 = 54 ml. After the second iteration you will be left with

2/3 × 54 = 36 ml. After the third iteration you will be left with

2/3 × 36 = 24 ml. After the fourth iteration you will be left with

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2/3 × 24 = 16 ml. So the required ratio will be 16 : (81 – 16) = 16 : 65

7. In a survey of defaulted payments of electrical bills of a residential complex of 125 houses, it is found that 50 houses defaulted on their payment of electrical bills in January, 60 in February and 40 in March. Houses can default in consecutive months only. 20 defaulted in January and February. 10 defaulted in February and March. How many houses defaulted in all the 3 months?

A. 3

B. 5

C. 7

D. 9

Explanation :

We use formula for intersection of three sets, keeping in mind that Jan ∩ Mar does not exist, since they are not consecutive months.

Let x be the number of people defaulting in all 3 months.

We get the equation as : 125 = 50 + 60 + 40 – 20 – 10 + x. Solving we get x = 5.

8. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 metres away from the tree the angle of elevation becomes 30°. The breadth of the river is

A. 40 m

B. 20 m

C. 30 m

D. 60 m

Explanation :

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Let the breadth of the river be x, Using tangent rule we get,

So x = 20

9. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1, 2 are 0.45, 0.05 and 0.50 respectively. Assuming that outcomes are independent, the probability of India getting at least 7 points is

A. 0.8750

B. 0.0624

C. 0.0875

D. 0.0250

Explanation :

Getting 7 points is possible in 2 cases.

Case 1: India wins all 4 matches.

Probability: (.5)4 = .0625.

Case 2: India wins any of the 3 matches and draws the remaining match. This can happen in total 4 ways. Probability: 4 x (.50)3 x (.05) = .025.

So, required probability: .0625 + .025 = .0875

10. Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it is

A. 1/5

B. 1/3

C. 2/5

D. None of these

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Explanation :

Joint probability of all not being able to solve it is

2/3*3/4*4/5=2/5

11. The total cost of 8 buckets and 5 mugs is Rs. 92 and the total cost of 5 buckets and 8 mugs is Rs. 77. Find the cost of 2 mugs and 3 buckets.

A. Rs. 35

B. Rs. 70

C. Rs. 30

D. Rs. 38

Explanation :

CP of 1 bucket = Rs. X

CP of 1 mug = Rs. Y

∴ 8x + 5y = 92………….. (i)

5x + 8y = 77 …………….(ii)

By equation (i) × 5 – equation (ii) × 8.

40x + 25y – 40x – 64y

= 460 – 616 ⇒ − 39y = - 156⇒ y = 4

From equation (i),

8x + 20 = 92 ⇒8x = 92 – 20 = 72 ⇒ x = 9

∴ CP of 2 mugs and 3 buckets

= 2 × 4 + 3 × 9 = 8 + 27 = Rs. 35

12. If 4x/3 + 2P = 12 for what value of P, x = 6?

A. 6

B. 4

C. 2

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D. 1

Explanation :

When x = 6, (4 * 6)/3 + 2P = 12

⇒ 8 + 2P = 12

⇒ 2P = 12 – 8 = 4

⇒ P = 2

13. What number must be added to the expression 16a2 – 12a to make it a perfect square?

A. 9/4

B. 11/2

C. 13/2

D. 16

Explanation :

a2 - 2ab + b2 = (a-b)2

∴ 16a2 – 12a = (4a)2 - 2*4a*3/2

Hence, on adding (3/2)2 = 9/4, expression will be a perfect square.

14. The straight line 2x + 3y = 12 passes through:

A. 1st, 2nd and 3rd quadrant

B. 1st, 2nd and 4th quadrant

C. 2nd, 3rd and 4th quadrant

D. 1st, 3rd and 4th quadrant

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Explanation :

The usual way to solve these type of questions is to put x = 0 once and find y coordinate. This would represent the point where the line cuts the Y axis.

Similarly put y = 0 once and find x coordinate. This would represent the point where the line cuts the X axis. Then join these points and you will get the graph of the line.

So when we put x = 0 we get y = 4.

When we put y = 0 we get x = 6.

So when we join these points we see that we get a line in 1st quadrant, which when extended both sides would go to 4th and 2nd quadrants. So option B.

15. In ΔABC, ∠A + ∠B = 65°, ∠B + ∠C = 140°, then find ∠B.

A. 40°

B. 25°

C. 35°

D. 20°

Explanation :

∠A + ∠B = 65°

∴ ∠C = 180° - 65° = 115°

∠B + ∠C = 140°

∴ ∠B = 140° - 115° = 25°

16. The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age?

A. 30 years

B. 38 years

C. 44 years

D. 42 years

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E. None of these

Explanation :

Total sum of man's age & his son's age =28 × 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man's age = (3/4) × 56 = 42

So, the correct answer is option D.

17. A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC.

A. θ

B. θ/2

C. 2θ

D. 3θ

Explanation :

∠B + ∠D = 180°

∠A + ∠C = 180°

∠BAC = ∠BCA ∠DAC = ∠DCA

∴∠DAB = ∠DCB = 90°

∠DAC = θ

∴∠ADE = 90° - θ = ∠CDE

∴ ∠ABC = 180° – 2(90° - θ) = 2θ

18. If tan θ + cot θ = 2, then the value of tan2θ + cot2θ is

A. 2

B. 1

C. √2

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D. 0

Explanation :

tan θ + cot θ = 2 , On squaring both sides,

(tan θ + cot θ)2 = 4, ⇒ tan2θ + cot2θ + 2 tan θ cot θ = 4,

⇒ tan2θ + cot2θ = 4 – 2 = 2 , [tan θ . cot θ = 1]

19. How many integers are there between 300 and 600 that are divisible by 9?

A. 33

B. 31

C. 28

D. 25

E. None of these

Explanation :

The sequence is 306,… 594

594=306+(n-1)9⇒288=(n-1)9⇒n=33

20. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively?

A. 166 : 22

B. 83 : 22

C. 83 : 44

D. 78 : 55

E. None of these

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Explanation :

Three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively.

Petrol : kerosene

(4 : 1 = 5)7

(5 : 2 = 7)5

(6 : 1 = 7)5

28 : 7 = 35

25 : 10 = 35

30 : 5 = 35

83 : 22

21. The respective ratio of radii of two right circular cylinders (A & B) is 2 : 5. The respective ratio of the heights of cylinders A and B is 3 : 1. What is the respective ratio of volumes of cylinders A and B?

A. 12 : 25

B. 9 : 25

C. 9 : 20

D. 3 : 5

E. 12 : 35

Explanation :

R1/R2/=2/5 H1/H2=3/1 V1/V2= (R1/R2)2 × ( H1/H2)= 12/25

22. Raja gives 30% of his salary to his mother, 40% of the remaining salary he invests in an insurance scheme and PPF in the respective ratio of 4 : 3 and the remaining he keeps in his bank account. If the difference between the amount he gives to his mother and that he invests in insurance scheme is Rs. 8400, how much is Raja’s salary?

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A. Rs. 60,000

B. Rs. 62,000

C. Rs. 64,000

D. Rs. 65,000

E. Rs. 54,000

Explanation :

Let Raja salary= R

Salary given to mother = 0.3 R

Money left=0.7 R

Now, Money invested in Insurance scheme= 0.7*0.4*4/7 R= 0.16 R

Difference of money in bank and with mother= 0.14R

Now, 0.14 R=8400, Hence R= 60,0000

23. A, B, C and D are four consecutive odd numbers and their average is 42. What is the product of B and D?

A. 1860

B. 1890

C. 1845

D. 1677

E. None of these

Explanation :

As there are As diff. Is same so average should lie between B and C so B is 41 & C is 43 so D must be 45 as we have to find the product of B and D so it would be 1845.

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24. A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?

A. 2/11

B. 8/11

C. 9/11

D. 3/11

E. None of these

Explanation :

Selecting 1 black ball out of 5 = 5C1 ways.Selecting on red ball out of 3 = 3C1 ways

The required probability = ( 5C1 × 3C1)/ 11C2 = 3/11

25. A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money.

A. 10%

B. 24%

C. 45%

D. 18%

E. 5%

Explanation :

Let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.

26. 7 cannibals of XYZ island, decide to throw a party. As you may be aware, cannibals are guys who eat human beings. The senior among them – Father Cannibal decides that any 6 of them will eat up one cannibal, then out of the remaining six – five of them will eat up one cannibal and so on till one is left.

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What is the time until one cannibal is left, if it takes one cannibal 3 hours to eat up one cannibal independently?

A. 7 hrs 11 min

B. 6 hrs 12 min

C. 7 hrs 21 min

D. 18 hrs 16 min

Explanation :

At the beginning 6 cannibals will eat one, so time required will be 180/6 = 30 min.

Then out of the remaining six – five will devour one, so time required will be 180/5 = 36 min.

Thus the time until one cannibal is left will be = (180/6 + 180/5 + 180/4 + 180/3 + 180/2 + 180/1) min

= (30 + 36 + 45 + 60 + 90 + 180) min

= 441 min

= 7 hrs 21 min.

Hence option 3.

27. Three articles are purchased for Rs. 1050, each with a different cost. The first article was sold at a loss of 20%, the second at 1/3rd gain and the third at 60% gain. Later he found that their SPs were same. What was his net gain/loss?

A. 14.28% gain

B. 13% loss

C. 12% loss

D. 11.11% gain

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Explanation :

Let us assume that their CPs are x, y & z respectively.

According to the given condition 0.8x = 1.33y = 1.6z

⇒ (80/100)x = 400y/(3 × 100) = (160/100)z

⇒ x : y = 5 : 3 & y : z = 6 : 5

Thus x : y : z = 10 : 6 : 5

Hence CPs of the articles are x = (10/21) × 1050 = 500,

y = (6/21) × 1050 = 300 &

z = (5/21) × 1050 = 250.

SP of the article with CP Rs. x is 0.8x = 0.8 × 500 = 400.

Since SPs are same, the total SP will be 400 × 3 = 1200.

Hence the gain % = (SP – CP)/CP × 100 = (1200 – 1050)/1050 × 100 = 14.28%.

28. In a game of tennis, A gives B 21 points and gives C 25 points. B gives C 10 points. How many points make the game?

A. 50

B. 45

C. 35

D. 30

Explanation :

When B scored p -10 then C scored p - 25.

When B scores 1 then C scores (p-25)/(p-10)

So when B scores p points then C will score (p-25)/(p-10) × p

As per question (p-25)/(p-10) × p = p -10 . Solving this we get p = 35

A B C

p points (p-21) points (p-25) points

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p points (p-10) points

29. What is the value of a if x3 + 3x2 + ax + b leaves the same remainder when divided by (x – 2) and (x + 1)?

A. 18

B. 3

C. -6

D. Cannot be determined

Explanation :

Suppose the remainder is R.

Substituting x = 2 and x = –1, we get R = 8 + 12 + 2a + b = –1 + 3 – a + b

⇒ 3a = –18

⇒ a = –6

30. What is the range of values of k if (1 + 2k)x2 – 10x + k – 2 = 0 has real roots?

A. –3 ≤ k ≤ 4.5

B. –1.5 ≤ k ≤ 9

C. k ≥ 4.5, k ≤ –3

D. k ≥ 3, k ≤ –9

Explanation :

Since the given expression has real roots, we know that (–10)2 – 4(1 + 2k)(k – 2) ≥ 0

100 – 8k2 + 12k + 8 ≥ 0

8k2 – 12k – 108 ≤ 0

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2k2 – 3k – 27 ≤ 0

–3 ≤ k ≤ 9/2

31. The sum of the first n terms of an AP is Sn = 4n2 – 2n. Three terms of this series, T2, Tm and T32 are consecutive terms in GP. Find m

A. 7

B. 10

C. 16

D. 5

Explanation :

From the given information, S1 = 4 × 12 – 2 × 1 = 2 => T1 = 2. Now, S2 = 4 × 22 – 2 × 2 = 12.

Since S2 = T1 + T2 and T1 = 2, we get T2 = 10. So, the 1st term of the AP is 2 and the common difference is 8.

From this, we get T32 = 2 + 31 × 8 = 250.

Since T2 , T3 and T32 are consecutive terms in GP, we know that Tm / T2 = T32 / Tm

⇒ (Tm )2 = T2 × T32 = 2500

⇒ Tm = 50.

32. A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total. If he sold one of the bullocks at a gain of 20%, the other is sold at a loss of

A. 20 %

B. 18%

C. 14%

D. 21 %

E. None of these

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Explanation :

A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total.

As he sold one bullocks at a gain of 20%, it means 120% of C.P = 8400

We get C.P of one bullock = 7000

So gain on one bullock = Rs 1400

Other bullocks is sold at lose and there is neither losing nor gaining in total

So loss on 2nd bullock = 1400/7000×100 = 20%

33. Two trains 130 and 110 meters long are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of the faster train.

A. 38 m/sec

B. 46 m/sec

C. 42 m/sec

D. 50 m/sec

Explanation :

Total Distance to be travelled by both the trains

= 130 + 110 = 240m

Let ‘F ’and ‘S’ be the speeds of fast and slow trains in m/sec. 240=60(F-S), 240= (F+S)

In the same direction , F – S = 4 m/sec ……(1)

In the opposite direction , F + S =80 m/sec……(2)

Solving them we get F = 42 m/sec.

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34. A motor boat can travel at 10 km/h in still water. It travelled 91 km downstream in a river and then returned, taking altogether 20 hours. Find the rate of flow of the river.

A. 6 km/hr

B. 5 km/hr

C. 8 km/hr

D. 3 km/hr

Explanation :

Given, speed of the Boat in still water (B)=10 km/hr

Let S be the speed of flow of river, then

91/(10+S) + 91/(10-S) = 20, Then going by options

91/13 - 91/7 = 20

So, S = 3 km/hr.

35. The total tractor population in a state is 2,94,000, out of which 1,50,000 are made by Mahindra & Mahindra. Out of every 1,000 Mahindra tractors, 98 are red in colour, but only 5.3% of the total tractor population is red. Find the percentage of non-Mahindra tractors that are red.

A. 0.5025%

B. 0.5130%

C. 0.6125%

D. 0.6140%

Explanation :

Total tractor population = 2,94,000

Mahindra & Mahindra = 1,50,000

So, Non Mahindra trucks = 1,44,000

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Since out of every 1000 Mahindra tractors, 98 are red, out of 1,50,000 Mahindra tractors 14,700 are red.

5.3% of 2,94,000 = 15,582 are red tractors in all.

So non Mahindra tractors which are red

=15,582 – 14,700 = 882

Hence percentage of non Mahindra tractors that are red = 882/144,000 * 100 = 0.6125%

36. 7% of the total quantity of wheat is lost in grinding when a country has to import 12 million tonnes, but when only 51⁄5 is lost, it can import 3 million tonnes. Find the quantity of wheat grown in the country.

A. 500 million tonnes

B. 400 million tonnes

C. 600 million tonnes

D. 700 million tones

Explanation :

Difference in % of wheat lost = 7 – 26/5 = 9/5%

Difference in import = 12 – 3 = 9 million As 9/5% % of total qty of wheat = 9 million

⇒ 9x/500 = 9

⇒ x = 500 million

37. A man who can swim 48 m/min in still water swims 200 m against the current and 200 m with the current. If the difference between those 2 times is 10 minutes, find the speed of the current.

A. 30 m/min

B. 29 m/min

C. 31 m/min

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D. 32 m/min

Explanation :

Try option & get answer as fourth option:

(200/(48 - 32)) - (200/ (48 + 32)) (12(1/2)min - 2(1/2)min)

= 10 min

38. A and B run a 5 km race on a round course of 400 m. if their speed be in the ratio 5 : 4, how often does the winner pass the other on circular track?

A. 4 times

B. 3 times

C. 5 times

D. 2 times

Explanation :

Total no. of round will be 5000/400 = 12.5

No. of rounds A completes to finish the race will be 12.5 and by the time B can complete only 10 rounds.

(As ratio of speed of A & B is 5 : 4. So they meet for the first time after A has finished 5 rounds and B has finished 4 rounds.)

So difference in no. of round will be = 21⁄2

The winner meets the other 2 times because the winner meets the other after every 2000 meters.

39. Mira’s expenditure and saving are in the ratio 3:2. Her income increases by 10%. Her expenditure also increases by 12%. By how much % do her saving increase?

A. 7%

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B. 9%

C. 10%

D. 13%

Explanation :

Let total income be = 5

Increased income will be = 5.5

Increased expenditure will be = 3.36

Increased saving will be = 5.5 – 3.36 = 2.14

Percentage increase will be = 14/2 * 100 = 7%

40. Two vessels contain spirit of 0.5 and 0.75 concentrations. If two liters from the first vessel and three liters from the second vessel are mixed, then what will be the ratio of the spirit and the water in the resultant solution?

A. 13 : 7

B. 15 : 17

C. 7 : 17

D. 17 : 15

Explanation :

Take 12, 12 liters in both mixtures which gives us

First

Spirit - 6

Water - 6

Second

Spirit - 9

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Water - 3

Taking 2 liters from 1st mixture and 3 liters from 2nd mixture which gives us

First

Spirit - 1

Water - 1

Second

Spirit - 9/4

Water - 3/4

So total of sprit and water in new mixture will be =

Spirit Water

1 + (9/4) 1 + (3/4)

13/4 7/4

Which will give 1st option as the answer.

41. Two small circular parks of diameters 16 m, 12 m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks?

A. 10

B. 20

C. 15

D. 25

Explanation :

(Some of areas of 2 smaller parks = New bigger one

π(8)² + π(6)² = πr²

π[64+36] = πr²

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π[100 = πr²

r= 10

42. The length of a rectangular field is double its width, inside the field there is a square-shaped pond 8 m long. If the area of the pond is 1/8 of the field, what is the length of the field?

A. 32 m

B. 16 m

C. 64 m

D. 20 m

Explanation :

Area of Pond = 64

Area of field = 64 × 8 = 512

Area of field ⇒ x . 2x = 512

⇒ 2x2 = 512 ⇒ x2 = 256 ⇒ x = 16

Length = 2 × 16 = 32. So A option is answer.

43. A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the oath is to be constructed with square marble tiles 20 cm × 20 cm, find the number of tiles required to cover the path.

A. 1800

B. 2000

C. 200

D. 2150

Explanation :

Area of field = 16 × 26 = 416 m2

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Area of inner field = 24 × 14 = 336 m2

Remaining area = 416 – 336 = 80 m2

Area in cm = 80 × 100 × 100 = 800,000 cm2

Area of each marble = 20 × 20 = 400

No. of tiles = 800000/400 = 2000

44. From the top of a cliff 25 m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower.

A. 40 m

B. 50 m

C. 48 m

D. 52 m

Explanation :

ZP is parallel to XY, so angle ZPY = angle ZYX,

And angle PZY = angle QZP

Hence angle QZP = ZYX = PZY

As ZXY is 90, so the only possible value that satisfy the above angles is 45

Then XY = 25 m, PZ = 25 and PQ = 25

As x = 450, total height of tower will be

= 25 + 25 = 50 m

45. A bath tub can be filled by a cold water pipe in 20 minutes and by a hot water pipe in 30 minutes. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath tub should be full. Finding however, that the waste pipe has been open, he now closes it. In 3 minutes more the bath tub is full. In what time would the waste pipe empty it?

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A. 38 min

B. 45 min

C. 42 min

D. 48 min

Explanation :

Total work = 1/20 + 1/30

(3+2)/60 = 5/60 = 1/12

For both of them needed = 12 min.

But due to leakage it take = 15 min.

So we can say for filling pipe it takes 3 minutes

work for the waste pipe will be = 12 min.

3 min. of both filling pipe = 12 min. of waste pipe

12 min. of filling pipe will be = 48 min. of waste pipe i.e. our answer is 4th option

46. A mixture of 45 liters of spirit and water contains 20% of water in it. How much water must be added to make the water 25% in the new mixture?

A. 5 litres

B. 3 litres

C. 4 litres

D. 6 litres

Explanation :

In Mixture Spirit Water

36 9

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On adding water in the mixture it becomes 25 % of mixture, so spirit will be 75 % of the mixture.

75% of Total = 36

⇒ Total = 36/0.75 = 48 liter. Hence 3 liter water is needed.

47. In a year 28th February is Tuesday; if the leap year is excluded, then 28th March will be a

A. Sunday

B. Tuesday

C. Monday

D. Saturday

Explanation :

Simple counting of days.

28th Feb = Tuesday

28th March = Tuesday

48. Ram’s age was square of a number last year and it will be cube of a number next year. How long must he wait before his age is again the cube of a number

A. 39 years

B. 38 years

C. 10 years

D. 64 years

Explanation :

First square then cube, this no will be after25, 27 years respectively. Next cube will be at 64 so he has to wait for 38 years

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49. Two small circular parks of diameters 16 m, 12 m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks?

A. 10

B. 20

C. 15

D. 25

Explanation :

Some of areas of 2 smaller parks

= New bigger one

π(8)² + π(6)² = πr²

π[64+36] = πr²

π[100 = πr²

r= 10

50. A bottle contains 3/4 of milk and the rest water. How much of the mixture must be taken away and replaced by equal quantity of water so that the mixture has half milk and half water?

A. 25%

B. 33.33%

C. 45%

D. 50%

Explanation :

Question can be solved by just putting value in Exp. Take total as 12 liter Quantity of milk & water will be 9, 3

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Take out 1/3rd of mixture out now we have quantity of milk & water will be 6, 2

Now replace with water we get quantity of mixture will be 6, 6 liters. This is the required answer (2nd option) because we have replaced mixture with 4 liters of water.

51. Two vessels contain spirit of 0.5 and 0.75 concentrations. If two liters from the first vessel and three liters from the second vessel are mixed, then what will be the ratio of the spirit and the water in the resultant solution?

A. 13 : 7

B. 15 : 17

C. 7 : 17

D. 17 : 15

Explanation :

Take 12, 12 liters in both mixtures which gives us

First

Spirit - 6

Water - 6

Second

Spirit - 9

Water - 3

Taking 2 liters from 1st mixture and 3 liters from 2nd mixture which gives us

First

Spirit - 1

Water - 1

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Second

Spirit - 9/4

Water - 3/4

So total of sprit and water in new mixture will be =

Spirit Water

1 + (9/4) 1 + (3/4)

13/4 7/4

Which will give 1st option as the answer.

52. A and B run a 5 km race on a round course of 400 m. if their speed be in the ratio 5 : 4, how often does the winner pass the other on circular track?

A. 4 times

B. 3 times

C. 5 times

D. 2 times

Explanation :

Total no. of round will be 5000/400 = 12.5 No. of rounds A completes to finish the race will be 12.5 and by the time B can complete only 10 rounds. (As ratio of speed of A & B is 5 : 4. So they meet for the first time after A has finished 5 rounds and B has finished 4 rounds.) So difference in no. of round will be = 21⁄2.

The winner meets the other 2 times because the winner meets the other after every 2000 meters.

53. A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?

A. 0

B. 89

C. -89

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D. None of these

Explanation :

Let S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6)

As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1)

f(2) = f(0) - 8

f(3) = f(1) - 15

f(4) = f(2) - 24 = f(0) - 32

f(5) = f(3) - 35 = f(1) - 50

f(6) = f(4) - 48 = f(0) - 80

Put the above values in equation (1), we get

S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80

S = 2(f(0) + f(1)) - 153 ------ (2)

As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32

Putting this value in equation 2, we get S = 2(32) - 153 = -89

So, Ans is option C.

54. In ΔABC, the internal bisectors of ∠ABC and ∠ACB met at I and ∠BAC = 50°. The measure of ∠BIC is

A. 105°

B. 115°

C. 125°

D. 130°

Explanation :

I is the In-centre

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So, ∠BIC = 90° + 1/2 ∠BAC

= 90° + 1/2 × 50 = 115°

55. The difference between [3/5] of [2/3] a number and [2/5] of[1/4] of the same number is 288. What is the number?

A. 960

B. 850

C. 895

D. 955

Explanation :

Let the no. Be [3/5] x [{2/3}x]-[2/5] x [1/4]x,then = 288 Solving it we will get 960

56. A, B, C and D are four consecutive odd numbers and their average is 42. What is the product of B and D?

A. 1860

B. 1890

C. 1845

D. 1677

E. None of these

Explanation :

As diff. Is same so average should lie between B and C so B is 41 & C is 43 so D must be 45 as we have to find the product of B and D so it would be 1845

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57. The cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?

A. Rs.450/-

B. Rs.420/-

C. Rs.400/-

D. Rs.350/-

E. Rs.480/-

Explanation :

The cost price of item B is Rs. 150/- more than the Let us assume cost price of A= X

So that Cost price of B= X+150.

SP of A= X*1.1

SP of B=(X+150)*0.8

Given that

SPA: SPB

11:12

So that 1.1X/(X+150)*0.8= 11/12

X=300

CP of B= 300+150=450

58. A sum of Rs 731 is divided among A, B and C such that 'A' receive 25% more than 'B' and 'B' receive 25% less than 'C'. What is C's share in the amount?

A. Rs. 172

B. Rs. 200

C. Rs. 262

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D. Rs. 258

E. None of these

Explanation :

A + B + C = 731 ..... (i)

A = 1.25B, gives A = 1.25 * 0.75 C = 0.9375 C....(ii)

B = 0.75C....(iii)

Using (ii) and (iii) in (i) we get

0.9375C + 0.75C + C = 731, gives C = 272.

So option E is the answer.

59. In how many different ways can letters of the word "PRAISE" be arranged?

A. 720

B. 610

C. 360

D. 210

E. None of these

Explanation :

As total number of alphabets in PRAISE are 6, so total no. of ways is 6!=720 So option A is the answer

60. If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 300%, the resultant fraction is [5/18]. What is original fraction?

A. 4/9

B. 4/5

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C. 8/9

D. 8/11

E. None of these

Explanation :

Let the fraction be [n/d] & after that it becomes [2.5n/4d]=5/18 . So we get the result as [4/9]

61. A car covers the first 30 km of its journey in 45 minutes and the remaining 25 km in 30 minutes. What is the average speed of the car?

A. 60

B. 64

C. 49

D. 48

E. None of these

Explanation :

Total distance/Total time =(30+25)/[(3/4)+(1/2)]

Average Speed=44kmph

62. Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days?

A. 8

B. 7.5

C. 10

D. 8.5

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E. None of The above

Explanation :

Examiners Days Hours/Day Papers

4 10 5 x

2 20 ? 2x

So, we required number of hours = so optionC is the answer

Using chain rule,

(4×10×5)/X= (2×20×Y)/2X

X=10 hrs/day

63. If 4x - 3y = 19 and x + 2y = 13, what are the respective values of x and y?

A. 5, 4

B. 6, 5

C. 7, 3

D. 8, 7

Explanation :

4x-3y=19, x+2y=13 Option 3rd satisfies all two equations

64. Due to global recession starting in January, Ram's monthly salary of Rs 8,000 was cut by 10%. The monthly expenses, which were Rs 6,000, increased at the rate of 5% per month. From which month will he have no savings if the recession lasted for a year?

A. May

B. April

C. March

D. June

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Explanation :

Month Salary Expenses Saving

January 7200 6000+ 5% of 6000 = 6300 7200-6300-900

February 7200 6300+5% of 6300= 6615 7200-6615=585

March 7200 6615+5% of 6615= 6945.75 7200-6945.75=254.25

April 7200 6945.75+ 5% of 6945.75 = 7293.0375 Expenses are more than salary

From April onwards, he will have no savings.

65. A hemispherical bowl is 176 cm round the brim. Supposing it to be half full, how many persons may be served from it in hemispherical glasses with diameter of 4 cm at the top?

A. 1372

B. 1272

C. 1172

D. 1472

Explanation :

Circumference of bowl = 176 = 2 π r ; r = 28

Quantity of liquid = ½ * (2/3 * π * 283) = 3 * 283 π.

Volume of a glass is = 2/3 *π * 23 = 16π/3.

Number of glasses = (3 * 283π / (16π/3)

= 1372

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66. A and B working together can complete a piece of work in 12 days. B and C working together can complete the same work in 16 days. A worked at it for 5 days and B worked at it for 7 days. C finished the remaining work in 13 days. How many days would C alone take to complete it?

A. 32

B. 24

C. 10

D. 40

Explanation :

1/A + 1/B = 1/12 and 1/B + 1/C = 1/16

= 5/A + 7/B + 13/C = (1/A + 1/B)5 + (1/B + 1/C )2 + 11/C = 1. Substituting from the above equations, we get

C = 24.

67. Sixteen men can complete a work in twelve days. Twenty-four children can complete the same work in eighteen days. Twelve men and eight children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work?

A. 6

B. 4

C. 2

D. None of these

Explanation :

Let the total work = 36

A man does 36/(12 * 16) = 3/16 work per day.

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A child does 36/(18 * 24) = 1/12 work per day.

12 men & 8 children do 12(3/16) + 8 (1/12) = 9/4 + 2/3

Now for 8 days, 8(9/4 + 2/3) = 70 / 3

The remaining work = 36 – (70/3) = 38/3

12 men and 11 children will complete the remaining work in x days.

x[(12 * 9/4) + (11 * 1/12)] = 38/3 * x = 4.

68. Two men A and B working together complete a piece of work which it would have taken them 30 and 40 days respectively to complete if they worked separately. If they received a payment of ` 21,000, B's share is

A. 8000

B. 12000

C. 9000

D. None of these

Explanation :

Let the amount of work be 120 units.

A would have done 4 units a day.

B would have done 3 units a day.

So the ratio when they work together = 4 : 3

From 21000, B' share will 3/7 Rs 21000 = 9,000.

69. If Rs 10 be allowed as true discount on a bill of Rs 110 due at the end of a certain time, then the discount allowed on the sum due at the end of double the time is

A. 22

B. 21.81

C. 20

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D. 18.33

Explanation :

Discount of Rs.10 on Rs.110 discount = 10%.

Bill= Rs.100

After the end of double the time, Bill = 200

So, 10 % of 200 = 20.

70. A man purchased a cycle for Rs 3,000 and sold it the same day for Rs 3,600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of

A. 7.5%

B. 5%

C. 20%

D. None of these

Explanation :

The rate of interest is 10%.

For 2 years, It will become 20% of 3600 = 720.

So he gain 720 + 600 = 1320 on 3000.

So a man has a gain of 44%.

71. The angle of elevation on the top of a tower from two horizontal points at distance of 'a' and 'b' metres from the tower are 'α' and '90 -α ' respectively. The height of the tower will be (where a > b)

A. ab metres

B. √ ab metres

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C. √ a/b metres

D. √ b/a metres

Explanation :

72. A person observes the angle of elevation of a building as 30°. The person proceeds towards the building with a speed of 25(√ 3 -1)m/hour. After 2 hours, he observes the angle of elevation as 45°. The height of the building (in m) is

A. 50 ( √ 3 +1)

B. 50

C. 100

D. 50 ( √ 3 -1)

Explanation :

73. A, B and C started a business by investing Rs. 12,800/-. Rs.16,800/- and Rs. 9,600/- respectively. If after 8 months B received Rs. 13,125/- as his share of profit, what amount did C get as his share of profit?

A. Rs. 7,800/-

B. Rs. 7,150/-

C. Rs. 7,750/-

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D. Rs. 8,250/-

E. Rs. 7,500/-

Explanation :

Here the profit will be distributed in the ratio of their investments

i.e. 12800:16800:9600 → 16:21:12

Let 'x' be the total profit

we know that profit received by B = 13125/-

Therefore,

21 / (16+21+12) * x = 13125

Share received by C = (12 / 49) * 30625 = 7500/-

74. 456 ÷ 24 * 38 - 958 + 364 = ?

A. 112

B. 154

C. 128

D. 136

E. 118

Explanation :

Applying BODMAS

? = 456 ÷ 24 * 38 - 958 + 364

= 19 * 38 - 958 + 364

= 722 - 958 + 364

= 1086 - 958

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= 128

Hence, the answer is option C.

75. (34.5 × 14 × 42) ÷ 2.8 =?

A. 7150

B. 7365

C. 7245

D. 7575

E. 7335

Explanation :

? = (34.5 × 14 × 42) ÷ 2.8

= 20286 / 2.8

= 7245

Hence, the answer is option C.

76. -676.76 + 1237.87 + 897.34 - ? = 1294.25

A. 168.6

B. 164.2

C. 156.4

D. 172.2

E. 158.6

Explanation :

Applying BODMAS

? = -676.76 + 1237.87 + 897.34 - 1294.25

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= 164.2

Hence, the answer is option B.

77. Pure milk costs Rs. 16/- per liter. After adding water the milkman sells the mixture @ Rs. 15/- per liter and thereby makes a profit of 25% in what respective ratio does he mix milk with water?

A. 3 : 1

B. 4 : 3

C. 3 : 2

D. 5 : 3

E. 4 : 1

Explanation :

If SP of mixture is 15/- per liter and profit is 25%, then

CP of mixture = (100/125) * 15 = 12/- liter

As 16/- is the cost of pure 1000 ml, therefore, for 12/-, the quantity of milk =

(12/16) * 1000 = 750 ml

So for 12/- per liter, the milk is 750 ml, then water will be 250 ml.

Thus, required ratio = 750:250 = 3:1

78. What will come in place of question mark (?) in the given question?

36 38.8 42.8 ? 54.4 62

A. 46.2

B. 46.6

C. 48.2

D. 48

E. 49

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Explanation :

Here the given pattern is as follows:

36 38.8 42.8 ? 54.4 62

+2.8 +4.0 +5.2 +6.4 +7.6

+1.2 +1.2 +1.2 +1.2

So ? = 42.8 + 5.2 = 48

79. A merchant bought some goods worth Rs. 6,000/- and sold half of them at 12% profit. At what profit percent should he sell the remaining goods to make an overall profit of 18%?

A. 24%

B. 28%

C. 18%

D. 20%

E. 26%

Explanation :

Let CPT = 6000/-

Therefore, cost of half of goods CP1= 3000/- and of other half goods = CP2= 3000/-

So, SP1=3000 × 1.12 = 3360/- and SPT= 6000 × 1.18 = 7080/-

Thus, SP2= 7080 – 3360 = 3720/-

Profit % = [(3720 - 3000) / (3000)] * 100 = 24%

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80. A firm of readymade garments makes both men's and women's shirts. Its profit average is 6% of sales. Its profits in men's shirts average 8% of sales and women's shirts comprise 60% of output. The average profit per sales rupee in women's shirts is

A. 0.0466

B. 0.0666

C. 0.0166

D. 0.0380

Explanation :

Let sales be Rs. 100 totally.

Of this Rs. 40 is sales of men's shirts.

Margin on that is 40 x 8% = Rs. 3.2

Now total margin is 100 x 6% = Rs. 6.

So margin from women's shirts is 6 – 3.2 = 2.8

This is from a sale of Rs. 60.

So profit per rupee sale is 2.8/60 = 0.047.

81. A student is to answer 10 out of 12 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A. 140

B. 280

C. 196

D. 346

Explanation :

4 questions can be chosen from the first 5 in 5 ways.

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Remaining 6 questions can be selected from 8 questions in 8C6 ways.

So required answer is 8C6 x 5 = 28 x 5 = 140.

82. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 courses are compulsory for every student?

A. 45 ways

B. 55 ways

C. 35 ways

D. 65 ways

Explanation :

7C3 = 35 as 2 cases are fixed.

83. Two cm rain has fallen on a sq. km of land. Assuming that 50% of the rain drops could have been collected and contained in a pool having a 100 m × 10 m base by what level would the water level in the pool has increased?

A. 15 m

B. 10 m

C. 20 m

D. 25 m

Explanation :

Volume of water collected = volume of pool

⇒ 1/2×2/100 × 1000 × 1000

= 100 × 10 × h

So h = 10 m is the answer.

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84. In a race of 600 metres, A can beat B by 60 metres and in a race of 500 metres, B can beat C by 25 metres. By how many metres will A beat C in a 400 metres race?

A. 50 m

B. 64 m

C. 54 m

D. 58 m

Explanation :

In 600 A beat B by 60 meter, so in a 400 m race the gap will be 40 only.

B beat C by 25 in 500; in 360 meter run he can beat C by 18 meter

So the total is 58 meter.

85. Two cards are drawn from a pack full of cards, in succession, with replacement. What is the probability that both are of different colours?

A. 1/2

B. 5/52

C. 2/13

D. 1/13

Explanation :

Probability for the first card = 52/52.

Probability for the second card will be = 26/52.

For both cards is =52/52 × 26/52 = ½.

Thus the first option is the answer.

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86. Two cards are drawn from a pack full of cards, in succession, with replacement. What is the probability that both are of different colours?

A. 1/2

B. 5/52

C. 2/13

D. 1/13

Explanation :

Probability for the first card = 52/52.

Probability for the second card will be = 26/52.

For both cards is =52/52 × 26/52 = ½.

Thus the first option is the answer.

87. In a coaching institute, every studentis selected in atleast one of the exam i.e. banking exam, and staff selection exam . 40 students are selected in the banking exam, 30 students are selected in the staff selection exam and 20 students are selected in both the examinations. How many students are there in the institute?

A. 45

B. 55

C. 50

D. 40

Explanation :

Banking exam = 40,

Staff exam = 30,

Both exam = 20

So banking only is 20, staff exam only is 10, and both is 20, so total is 50

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88. In two alloys, Copper and Zinc are related in the ratio of 4 : 1 and 1 : 3. 10 kg of 1st alloys, 16 kg of 2nd alloy and some pure copper are melted together. An alloy was obtained in which the ratio of copper to zinc was 3 : 2. Find the weight of the new alloy.

A. 35 kg

B. 45 kg

C. 40 kg

D. 50 kg

Explanation :

Copper Zinc

Ist alloy 8 2

2nd alloy 4 12

3rd alloy? = 9 0

Final Sol 21 (7 x 3) 14 (7 x 2)

89. An instruments manufactured by a company consists of two parts A and B. In manufacturing part A, 9 out of 100 are likely to be defective and in manufacturing part B, 5 out of 100 are likely to be defective. Calculate the probability that the instrument will not be defective.

A. 0.91

B. 0.86

C. 0.95

D. 0.83

Explanation :

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Probability of Non-defective part in A is = 91/100

Probability of Non-defective part in B is = 95/100

Overall non-defective part will be possible only when both components are non-defective.

Hence required probability is 0.91 x 0.95 = 0.86

90. A cricketer played 80 innings and scored an average of 99 runs. His score in the last inning was zero run. To have an average of 100 at the end, his score in the last innings should have been

A. 60 runs

B. 80 runs

C. 10 runs

D. 1 run

Explanation :

Let x be the score in the last inning to make the average of 100

Therefore, when average is 99, total score of 80 innings = 80 × 99 = 7920

And when the average is 100, total score of 80 innings = 80 × 100 = 8000

Therefore, x = 8000 – 7920 = 80

91. A man spends an average of Rs. 1,694.70 per month for the first 7 months and Rs.1,810.50 per month for the next 5 months. His monthly salary if he saves Rs. 3,084.60 during the whole year is

A. Rs. 1,000

B. Rs. 2,000

C. Rs. 2,400

D. Rs. 3,000

Explanation :

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Monthly salary = (1694.70 x 7 + 1810.50 x 5 +3084.60 / 12)

= (24000 / 12)

=2000/-

92. A and B undertake to do a piece of work for Rs. 2,200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days. Find C’s share.

A. Rs. 150

B. Rs. 275

C. Rs. 245

D. Rs. 175

Explanation :

Let 1 be the total work

Therefore, C's one Day work = (1 / 3) - ( (1 / 8) + (1 / 6) )

=1/24

Ratio of share of A, B and C

i.e A : B : C = (1/8) : (1/6) : (1/24)

⇒ 3 : 4 : 1

So, C's share = (1/8) x 2200 = 275 /-

93. By selling an article at 80% of its marked price, a trader makes a loss of 10%. What will be the profit percentage if he sells it at 95% of its marked price?

A. 5.9

B. 12.5

C. 6.9

D. 4.5

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Explanation :

Let us assume the MP to be 900/-

Therefore, SP = 80% of MP = 0.80 × 900 = 720/

As loss is 10%, so CP = 720/90 × 100 = 800/-

Now, if SP = 95% of MP = 0.95 × 900 = 855/-

Profit% = (855-800)/800 × 100 = 55/8 = 6.875 ≈ 6.9

94. By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% of the marked price. His gain during the sale season is

A. 8

B. 9

C. 7

D. 7.5

Explanation :

Given that SP of umbrella = 30/- and profit% = 20.

Therefore, CP of umbrella = 30/120 × 100 = 25/- SP of umbrella after 10% discount = 90/100 × 30 = 27/- Thus, profit% = (27 - 25)/25 × 100 = 8

95. From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?

A. 4 : 1

B. 4 : 5

C. 5 : 2

D. 1 : 4

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Explanation :

Let x and y be the two numbers, with x > y

Now are given that x - y/2 = 4[y - y/2]

Solving the above equation, we get x/y = 5/2

96. Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages per person are in the proportion of 5 : 3 : 2. When 90 men are employed, total daily wages of all amounts to Rs. 10,350. Find the daily wage of a man.

A. Rs. 115

B. Rs. 75

C. Rs. 45

D. Rs. 57.50

Explanation :

Let the daily wages be 5k, 3k and 2k of men, women and children respectively.

We are given that there are 90 men and total amount of wages is 10350/-

Thus, men, women and children are 90, 60 and 30 respectively.

Hence, total wages = 90 x 5k + 60 x 3k + 30 x 2k = 10350

⇒ k = Rs.15

Thus, daily wages of each man = 5k = Rs.15 x 5 = Rs. 75

97. The population of a town is 3,11,250. The ratio between women and men is 43 : 40. If there are 24% literate among men and 8% literate among women, the total number of literate persons in the town is

A. 56,800

B. 99,600

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C. 41,800

D. 48,900

Explanation :

Total number of literate people is 24 % of men and 8 % of women.

Therefore, No of literate persons = (24/100 × 40/83 × 311250) + (8/100 × 43/83 × 311250) = 48900

98. In an examination, 52% of the candidates failed in English and 43% failed in Mathematics. If 17% failed in both the subjects, then the percentage of candidates, who passed in both the subjects, was

A. 15

B. 22

C. 23

D. 21

Explanation :

% of students failed in Mathematics only = 43% – 17% = 26%

% of students failed in English only = 52% – 17% = 35%. So % of students passed in both = 100 – (26 + 35 + 17) = 100 – 78 = 22%

Alternate Solution:

% of students failed in Mathematics or English or both = 52% + 43% – 17% = 78%

So % of students passed in both = 100% – 78% = 22%. Hence, option B is correct.

99. A is thrice as efficient as B and takes 10 days less to do a piece of work than B takes to do the same work. In how many days, B alone can finish the whole work?

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A. 15 days

B. 10 days

C. 9 days

D. 8 days

E. 7 days

Explanation :

Efficiency A:B = 3:1

Therefore, no. of days A:B = 1:3

Given, 3x – x = 10

Solving, A = 5 days and B= 15 days.

100. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is ________

A. Rs. 400

B. Rs. 500

C. Rs. 600

D. Rs. 800

E. Rs 550

Explanation :

Let 'P' be the principle

P(1.1)2 – P = 525

P = 2500

S.I = (2500*4*5)/100 = 500

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101. The cost price of item B is Rs. 150/- more than the cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?

A. Rs. 450/-

B. Rs. 420/-

C. Rs. 400/-

D. Rs. 350/-

E. Rs. 480/-

Explanation :

Let us assume cost price of A= X

So that Cost price of B= X+150.

SP of A= X*1.1

SP of B=(X+150)*0.8

Given that

SPA: SPB

11:12

So that 1.1X/(X+150)*0.8= 11/12

X=300

CP of B= 300+150=450

102. A vessel contains a mixture of milk and water in the respective ratio of 10: 3. Twenty-six litres of this mixture was taken out and replaced with 8 litres of water. If the resultant respective ratio of milk and water in the mixture was 5 : 2, what was the initial quantity of mixture in the vessel? (in litres)

A. 143

B. 182

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C. 169

D. 156

E. 130

Explanation :

26 L mixture is taken out.

Quantity of Milk is taken out= 26*(10/13)=20

Quantity of Water is taken out=26*(3/13)=6

As we know that,

(10X-20)/(3X-6+8)=5/2

X=10,

Initial quantity of mixture in the vessel is= 13*X=13*10=130L.

103. There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number?

A. 31

B. 27

C. 29

D. 25

E. 33

Explanation :

Let the 6 consecutive odd no.'s are:

X, X+2, X+4,X+6, X+8, X+10

Avg. of 1st three no’s is X+2.

Avg. of Last three no’s is X+8.

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Given that (X+8)2-(X+2)2=288

X=19

Last odd no. is X+10= 29.

104. In a bag there are 6 red balls and 9 green balls. Two balls are drawn at random, what is the probability that at least one of the balls drawn is red?

A. 29/35

B. 7/15

C. 23/35

D. 2/5

E. 19/35

Explanation :

Probability of at least one of the balls drawn is red= 1- (9/15)*(8/14) =23/35.

DIRECTIONS for question 7 to 9: Study the following information and answer the question.

What approximate value will come in place of the question mark (?) in the given question? (You are not expected to calculate exact value)

105. ?% of 750.11 × 34.90 +6.995 = 3000

A. 15

B. 16

C. 11

D. 6

E. 19

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Explanation :

X% of 750 *34+7=3000

11.40. (approx)

106. 815.002 +29.98 – 53.998 + 3.012= ?

A. 800

B. 880

C. 840

D. 900

E. 750

Explanation :

815+30-54+32=?

800. (approx)

107. 40.1% of 360.2 + 58.98% of ? = 150

A. 10

B. 20

C. 30

D. 40

E. 50

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Explanation :

40*360+59%of X=150

144+59%of X=150

X=10(approx)

108. A is thrice as efficient as B. A started working and after 4 days he was replaced by B. B then worked for 15 days and left. If A and B together finished 75% of the total work, in how many days B alone can finish the whole work?

A. 27

B. 45

C. 24

D. 36

E. 42

Explanation :

A = 3B, Given:

4A + 15B = ¾ W => 27B = ¾ W

=> B = 36 days.

109. A toothpaste manufacturer is giving two different offers on its 100 g tube. The first one is giving 30% extra at the same price, and the second one is giving 30% off on the marked price. By what percentage is the first offer costlier than the second one?

A. 4.2%

B. 2.4%

C. 9.89%

D. 0%

Explanation :

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Suppose the price of the toothpaste is Rs. 10. In the first offer, the price per gram would be Rs. 10/130 while in the second offer, the price per gram would be Rs. 7/100.

So the first offer is costlier than the second offer by 10/130 – 7/100 = Rs. 9/1300. Hence the first offer is costlier than the second one by 9/1300 ÷ 7/100 × 100 = 9.89%.

110. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood.

A. 82125 cu. Cm

B. 81775 cu. Cm

C. 81000 cu. Cm

D. None of the above

Explanation :

Required volume = Outer volume of the box - Inner volume = (120 × 80 × 40) – (115 × 75 × 35) = 82125 cu. cm.

111. From the top of a light house 60 meters high with its base at the sea level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is (in m)

A. (√3-1)/(√3+1) × 60

B. (√3+1)/(√3-1) × 60

C. (√3+1)/(√3-1)

D. (√3-1)/(√6-1)

Explanation :

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112. The area of the triangle formed by the tangents from the point (4,3) to the circle x2 + y2 = 9 and the line joining their points of contact is:

A. 25/192 square units

B. 192/25 square units

C. 385/25 square units

D. 185/25 square units

Explanation :

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113. The Hussain Sagar Express travels from Mumbai to Hyderabad. Along the way the train stops at 18 different places. So, in total, there are 20 stops including stop at Mumbai and Hyderabad. How many different tickets can be given out by the railways?

A. 190 different tickets

B. 380 different tickets

C. 145 different tickets

D. 120 different tickets

Explanation :

As there are 20 stations in total, so number of tickets = 20P2 = 380.

6. Sea water contains 5% salt by weight. How many kilograms of fresh water must be added to 40 kg of sea water so that the salt content of the solution becomes 2%?

A. 60 kg

B. 50 kg

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C. 40 kg

D. 55 kg

Explanation :

5% salt by weight means 2 kgs out of 40 kgs is salt.

Let x be the total amount of mixture

Therefore, 2% of x = 2 → x = 100 kg

So the amount of fresh water to be added in the mixture is 100 – 40 = 60 kg

114. A spherical ball 6 cm in diameter is melted and recast into 3 smaller spherical balls. The radius of the two of the there are 1.5 cm and 2 cm respectively. The radius of the third is

A. 3.5cm

B. 3.0cm

C. 2.0cm

D. 2.5cm

Explanation :

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115. 18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of 2 : 1. If the resultant respective ratio of milk and water in the vessel was 4 : 1, what was the quantity of pure milk added in the vessel? (in litres)

A. 4

B. 8

C. 10

D. 12

E. 2

Explanation :

80(M) + 18(W) = 98

49 liters sold => 49 is left

40(M) + 9(W)

Let x be the quantity of pure milk added

Given, (40 + 2x)/(9 + x) = 4/1

Solving, x = 2

116. The respective ratio of radii of two right circular cylinders (A and B) is 4 : 5. The respective ratio of volume of cylinders A and B is 12:25. What is the respective ratio of the heights of cylinders A and B?

A. 2 : 3

B. 3 : 5

C. 5 : 8

D. 4 : 5

E. 3 : 4

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Explanation :

Volume = πr2h

π*4*4*hA / π*5*5*hB = 12/25

Solving, hA/ hB = 3:4

117. Dhruva gave 35% of her monthly salary to her mother. From the remaining salary, she paid 18% towards rent and 42% she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 43,920. What was her monthly salary?

A. Rs. 80,000

B. Rs. 75,000

C. Rs. 64,000

D. Rs. 76,000

E. Rs. 72,000

Explanation :

Let ‘x’ be the monthly salary, then

(65/100 × 40/100)x + 35/100x = 43920

Solving, X= 72000

DIRECTIONS for the questions 4-6: What approximate value will come in place of question mark (?) in the given question?( You are not expected to calculate the exact value.)

118. 26.003 - (154.001/6.995) = ?

A. 4

B. 18

C. 9

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D. 10

E. 14

Explanation :

26 – (154/7) = 4

119. 17.995/3.01 + 104.001/12.999 = ?

A. 11

B. 20

C. 23

D. 14

E. 17

Explanation :

18/3 + 104/13 = 14

120. 3/5 of 4/7 of 7/9 of 425 = ?

A. 121

B. 110

C. 118

D. 113

E. 124

Explanation :

3/5*4/7*7/9*425 = 113

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121. A number is such that when it is multiplied by ‘8’, it gives another number which is as much more than 153 as the original number itself is less than 153. What is 25% of the original number?

A. 8

B. 7.5

C. 10

D. 8.5

E. 6.5

Explanation :

Let the no. be X

Given 8X-153=153-X

Hence X=34

25% of X=8.5

122. A and B can complete a piece of work in 80 days and 120 days respectively. They started working together but A left after 20 days. After another 12 days C joined B and they completed the work in 28 more days. In how many days can C alone complete the work?

A. 110 days

B. 112 days

C. 114 days

D. 120 days

Explanation :

E. None of these

So efficiency of A and B are 3 units and 2 units respectively.

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As they worked for 20 days together after that A left so total unit contribution in 20 days= (3+2) units * 20 days = 100 units

Remaining units = 240 – 100 = 140 units

After another 12 days C joined B and they completed the work in 28

more days, so total units contribution of B in 40 days = 2*40 = 80 units

Remaining units i:e = 140-80 = 60 units

Now 60 units is done by C in 28 days

So to do 240 units C require = 28/60 *240 = 112 days

123. A man sets out on cycle from Delhi to Faridabad, and at the same time another man starts from Faridabad on cycle for Delhi. After passing each other they complete their journeys in 2 6 7 and 5 3 5 hours respectively. At what rate does the second man cycles if the first man cycles at 14 kmph?

A. 10 kmph

B. 5 kmph

C. 7 kmph

D. 8 kmph

E. None of these

Explanation :

Speed1/speed2 =√time2/√time1

14 km/h/speed2 = √535/√267

We get Speed2 =√97.81 = 9.88 km/h

124. In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number ofquestions, he answered correctly was:

A. 82

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B. 80

C. 68

D. 60

E. None of these

Explanation :

Total questions = 200

Attempted questions = 200

The student scores 4 marks for every correct answer and loses 1 mark for every

wrong answer and he scored 200 marks.

Maximum marks = 200×4 = 800

Scored marks = 200

So marks deducted = 800-200 = 600

For each wrong answer 5 marks are deducted.

So total wrong answers = 600/5 = 120

125. There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number?

A. 31

B. 27

C. 29

D. 25

E. 33

Explanation :

Let the 6 consecutive odd no.’s are:

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X, X+2, X+4, X+6, X+8, X+10

Avg. of 1st three no’s is X+2.

Avg. of Last three no’s is X+8.

Given that (X+8)2-(X+2)2=288

X=19

Last Odd no. is X+10= 29.

126. In a bag there are 6 red balls and 9 green balls. Two balls are drawn at random, what is the probability that at least one of the balls drawn is red?

A. 29/35

B. 7/15

C. 23/35

D. 2/5

E. 19/35

Explanation :

Probability of atleast one of the balls drawn is red= 1- (9/15) x (8/14)=23/35.

127. A started a business with an investment of Rs. 28,000. After 5 months from the start of the business, B and C joined with Rs. 24,000and Rs. 32,000 respectively and withdrew Rs. 8000 from the business. If the difference between A’s share and B’s share in the annual profit is Rs. 2,400, what was the annual profit received?

A. Rs. 15,600

B. Rs. 14,400

C. Rs. 14,040

D. Rs. 15,360

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E. Rs. 13,440

Explanation :

Equivalent Contribution of A= 28000 x5+20000 x 7= 280000

Equivalent Contribution of B= 24000x 7= 168000

Equivalent Contribution of C= 32000 x 7= 224000

Let total profit be X.

Given that,

280000X/672000 – 168000X/672000=2400

112000/672000 x X=2400

or X=2400 x 672/112

X=14400

128. At present, Ami’s age is twice Dio’s age and Cami is two years older than Ami. Two years ago, the respective ratio between Dio’s age at that time and Cami’s age at that time was 4 : 9. What will be Ami’s age four years hence?

A. 40 years

B. 30 years

C. 42 years

D. 36 years

E. 48 years

Explanation :

D; A = 2D; C = A+2 = 2D+2

Given, D-2/(2D+2)-2 = 4/9

Solving, D = 18 Years and A = 36+4 = 40 years.

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129. A and B can complete a piece of work in 80 days and 120 days respectively. They started working together but A left after 20 days. After another 12 days C joined B and they completed the work in 28 more days. In how many days can C alone complete the work?

A. 110 days

B. 112 days

C. 114 days

D. 120 days

E. None of these

Explanation :

So efficiency of A and B are 3 units and 2 units respectively.

As they worked for 20 days together after that A left so total unit contribution in 20 days= (3+2) units * 20 days = 100 units

Remaining units = 240 – 100 = 140 units

After another 12 days C joined B and they completed the work in 28

more days, so total units contribution of B in 40 days = 2*40 = 80 units

Remaining units i:e = 140-80 = 60 units

Now 60 units is done by C in 28 days

So to do 240 units C require = 28/60 *240 = 112 days

130. In a mathematics exam, a student scored 30% in the first paper out of a total of 180. How much should he score in the second paper (out of 150) if he is to get at least 50% marks overall?

A. 75%

B. 80%

C. 74%

D. 84%

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Explanation :

(30/100) x 180 + (x/100) x 150 = (50/100) x 330 ⇒ x = 74

131. If 15 men or 24 women or 36 boys can do a piece of work in 12 days, working 8 hours a day, how many men must be associated with 12 women and 6 boys to do another piece of work 21⁄4 times as great in 30 days working 6 hours a day?

A. 4

B. 8

C. 6

D. 10

Explanation :

Total man days = 15 x 12 x 8

= (x + (15/2) + (15/6) x 6 x (4/9) ⇒ x = 8

132. Two cogged wheels of which one has 16 cogs and the other 27, work into each other. If the latter turns 80 times in three-quarters of a minute, how often does the other turn in 8 seconds?

A. 18

B. 30

C. 24

D. 36

Explanation :

No of times the 16 cogs wheel size move in 8 seconds is (27 * 80)/45 * 8/16

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133. A milkman buys milk contained in 10 vessels of equal size. If he sells his milk at Rs. 5 a litre, he loses Rs. 200. If he sells it at Rs. 6 a litre, he would gain Rs. 150 on the whole. Find the number of litres contained in each vessel.

A. 20 litres

B. 30 litres

C. 25 litres

D. 35 litres

Explanation :

Let the Milk purchased be x

Let the Total Cost of Purchasing be x litre milk be y

When x Litre milk is sold for Rs. 5 the loss is Rs. 200

the equation can be written as:

y - 5x = 200

When x Litre milk is sold for Rs. 6 the profit is Rs. 150

the equation can be written as:

6x - y = 150

By solving the two equations:

y - 5x = 200

-y + 6x = 150

we get x = 350Litres. For 10 vessels we can have 35 litres

134. 16 January 1997 was a Thursday. What day of the week was 4 January 2000?

A. Tuesday

B. Wedsday

C. Thursday

D. Friday

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Explanation :

16th Jan 1997 – Thursday

16th Jan 1998 – Friday

16th Jan 1999 – Saturday

4th Jan 2000 – Tuesday

135. Out of a group of swans, 7/2 times the square root of the number are playing on the shore of a pond. The remaining two are inside the pond. What is the total number of swans?

A. 10

B. 14

C. 12

D. 16

Explanation :

7√x / 2 + 2 = x

Check by option.

136. A wooden box of dimensions 8 m × 7 m × 6m is to carry rectangular boxes of dimension: 8 cm × 7 cm × 6 cm. The maximum number of boxes that can be carried in the wooden box is

A. 98,00,000

B. 10,00,000

C. 75,00,000

D. 12,00,000

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Explanation :

(800 x 700 x 600 / 8 x 7 x 6) = 10,00,000

137. The horizontal distance between two towers is 60 m. The angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, the height of the shorter one is

A. 116 m

B. 216 m

C. 200 m

D. None of these

Explanation :

tan30 = (150 - x /60) ⇒(1/√3) = (150 - x/60)

On Solving, we get x = 116

138. An aeroplane travels distances of 2500 km, 1200 km and 500 km at speeds of 500 km/hr, 400 km/hr and 250 km/hr respectively. The average speed is

A. 420 km/hr

B. 405 km/hr

C. 410 km/hr

D. 575 km/hr

Explanation :

Total distance = 2500 + 1200 + 500 = 4200 km

Total time taken = 2500/500 + 1200/400 + 500/250 = 10

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Avg speed = Total distance/Total Time Taken = 4200/10 = 420 km/hr

139. A and B are partners in a business. They invest in the ratio 5:6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B's investment was used?

A. 12 months

B. 10 months

C. 15 months

D. 14 months

E. 18 months

Explanation :

Ratio of profit is always distributed in the ratio of their investment and time.

5unit × 8 months:6 units × B’s months = 5:9

So B’s investment time = 12 months

140. There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly. Find probability that 1 is red and the other is white.

A. 5/22

B. 5/23

C. 7/22

D. 4/9

E. None of these

Explanation :

There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly.

probability that 1 is red and the other is white = 3/12× 5/11 = 5/44

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141. According to a new plan rolled out by H1SP Bank, the rate of simple interest on a sum of money is 8% p.a. for the first two years, 10% p.a. for the next three years and 6% p.a. for the period beyond the first five years. Simple interest accrued on a sum for a period of eight years is Rs. 12,800. Find the sum.

A. Rs. 24,000

B. Rs. 16,000

C. Rs. 15,000

D. Rs. 13,500

E. None of these

Explanation :

Let the sum of money be x.

So interest in first two years = 8×2 = 16% of x

Interest in next three years = 10×3 =30% of x

Interest in next five years = 6×3 = 18% of x

Total interest = 64% of x = Rs 12,800

We get x = Rs 20,000

142. Three Science classes A, B and C take a Life Science test. The average score of students of class A is83. The average score of students class B is 76. The average score of class C is 85. The average score of class A and 8 is 79 and average score of class B and C is 81. Then the average score. Of classes A, B and C is

A. 80

B. 80.5

C. 81

D. 81.5

E. None of these

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Explanation :

A:B:C = 3:4:5

Sum of A+B+C = 3*83+4*76+5*85 = 978

Average score = 978/12 = 81.5

143. A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?

A. 221

B. 343

C. 81

D. 243

E. None of these

Explanation :

Area of a hemispherical bowl = 2/3 ×π ×r3

Area of a cylinder = πr2h

Area of a cylinder = n × Area of a hemispherical bowl

2/3 ×π ×273 = n ×π×32×9

we get n = 162

DIRECTIONS for the questions 6 & 10: What approximate value will come in place of question mark (?) in the given question?( You are not expected to calculate the exact value.)

144. 26 .00 - (154.001/6.995) = ?

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A. 4

B. 18

C. 9

D. 10

E. 14

Explanation :

26 – (154/7) = 4

145. 17.995/3.01 + 104.001/12.999 = ?

A. 11

B. 20

C. 23

D. 14

E. 17

Explanation :

18/3 + 104/13 = 14

146. 3/5 of 4/7 of 7/9 of 425 = ?

A. 121

B. 110

C. 118

D. 113

E. 124

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Explanation :

3/5*4/7*7/9*425 = 113

147. 124.001 14.001 ÷ 3.4999 + 22 = ?

A. 500

B. 450

C. 425

D. 475

E. 550

Explanation :

124*(14/3.5)+ 4 = 500

148. 18.0009 ÷ √ (369 + ?) = 2040.05

A. 302

B. 298

C. 322

D. 319

E. 311

Explanation :

18/√36 * (369 + ?)= 2040.05

3(369+?)=2040

?=311

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149. A number x when divided by 289 leaves 18 as a remainder. The same number when divided by 17 leaves y as a remainder. The value of y is

A. 3

B. 1

C. 5

D. 2

Explanation :

Here, the first divisor (289) is a multiple of second divisor (17)

∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1. Hence the answer is option B

150. An equation of the form ax + by + c = 0 where a ≠ 0, b ≠ 0, c = 0 represents a straight line which passes through

A. (0, 0)

B. (3, 2)

C. (2, 4)

D. None of these

Explanation :

Ax+by+c = 0

When c = 0

ax+by = 0

by = -ax ⇒ y = - ax/b

when x = 0, y = 0 i.e., this line passes through the origin (0,0).

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151. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

A. -4/8

B. 2/7

C. 3/8

D. 3/7

Explanation :

Original fraction = (x - 4)/x

In case II,

8(x - 4 - 2) = x + 1

⇒ 8x - 48 = x + 1

⇒ 7x = 49 ⇒ x = 7

∴Original fraction

= (7 - 4)/7 = 3/7

152. Determine the probability that a digit chosen at random from the digits 1, 2, 3, ....., 9 will be a multiple of 3.

A. 1/5

B. 1/3

C. 2/5

D. 3/5

E. 4/7

Explanation :

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Total possible outcomes = 9. Favorable outcomes = 3. (i.e. 3, 6 OR 9 one out of three)

Probability =3/9 = 1/3

153. What is the probability that a coin will turn up heads at least once in six tosses of a coin?

A. 11/53

B. 41/53

C. 63/64

D. 1/64

E. None of these

Explanation :

Reqd. Probability = 1 - Probability of Not Getting Even One Head = 1 - (1/64) =63/64

154. The simple interest on Rs. 4000 in 3 years at the rate of x% per annum equals the simple interest on Rs. 5000 at the rate of 12% per annum in 2 years. The value of x is

A. 8%

B. 9%

C. 10%

D. 6%

155. Even after reducing the marked price of a transistor by Rs. 32, a shopkeeper makes a profit of 15%. If the cost price be Rs. 320, what percentage of profit would he have made if he had sold the transistor at the marked price?

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A. 25%

B. 20%

C. 10%

D. 15%

E. None of these

Explanation :

Let x be the marked price,

So x - 32 = 320 × 1.15 ⇒ x = 400.

So required value is

400 = 320 (1 + profit/100),

So profit is 25%

156. The sum of five numbers is 260. The average of first two numbers is 30 and average of the last two numbers is 70. What is third number?

A. 33

B. 60

C. 75

D. Can't determined

E. None of these

Explanation :

(a + b + c + d + e)/5 = 260 ...........(1)

(a + b)/2 = 30 , Therefore a + b = 60

(d + e)/2 = 70 , Therefore d + e = 140

Using the values in (1) , We get

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c= 60

As sum of first two is 60 & sum of last two is 140 so third no. is 260 - 60 - 140 = 60.

157. 20 boys and 32 girls form a group for social work. During their membership drive same no. of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 3:4 respectively?

A. 75

B. 86

C. 68

D. 82

E. None of these

Explanation :

Let x be the new boys as well as girls , Therefore

Solving this we get x = 16

So total will be 36 + 48 = 84

158. A copper wire is bent in the form of an equilateral triangle and has area 121√3cm2 . If the same wire is bent into the form of a circle. The area (in cm2) enclosed by the wire is (take π - 22/7)

A. 364.5

B. 693.5

C. 346.5

D. 639.5

E. None of these

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159. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively?

A. 166 : 22

B. 83 : 22

C. 83 : 44

D. 78 : 55

E. None of these

Explanation :

Three identical vessels in the ratio 4:1, 5:2 and 6:1 respectively. Petrol : kerosene (4 : 1 = 5)7 (5 : 2 = 7)5 (6 : 1 = 7)5 28 : 7 =35 25 : 10 =35 30 : 5 =35 83 : 22

160. Mrs. Sharma invests 15% of her monthly salary, i.e., Rs. 4428 in Mutual Funds. Later she invests 18% of her monthly salary on Pension Policies also she invests another 9% of her salary on Insurance Policies. What is the total monthly amount invested by Mrs. Sharma?

A. Rs. 113356.8

B. Rs. 12398.4

C. Rs. 56678.4

D. Can't determined

E. None of these

Explanation :

15% of monthly salary = Rs 4428

So monthly salary = Rs 29500

Total money invested = 42% of 29500 = Rs 12398.4

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161. At present, Aanshi is five years younger to Binny. Binny’s age twenty- years hence will be equal to twice of Aanshi’s age five years ago. What will be Binny’s age eight year hence?

A. 42 years

B. 35 years

C. 30 years

D. 48 years

E. None of these

Explanation :

Let age of Aanshi be A, Bunny be B.

According to equation, A= B-5

Also, B+20 = 2(B-10)

Solving these we get, B= 40. So after 8 years, his age will be 48 years.

162. In a bag, there are 8 red balls and 7 green balls. Three balls are picked at random. What is the probability that two balls are red and one ball is green in colour?

A. 28/65

B. 22/65

C. 37/65

D. 3/13

E. 1/13

Explanation :

Probability that two balls are red and one ball is green in colour = 8*7*7*3! / 15*14*13*2! = 28/65

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163. A vessel contains 120 litres of mixture of milk and water in the respective ratio of 11 : 4. Forty-five litres of this mixture was taken out and replaced with 5 litres of water. What is the percentage of water in the resultant mixture?

A. 1.35

B. 31.25

C. 25

D. 20

E. 15

Explanation :

Total volume 120 litres

Milk Water

88 32

if 45 litres of mixture is removed 5/8 of the mixture is left

Milk Water

55 20

Milk Water

55 25

% of water in the mixture= 25*100/ 80 = 31.25%

164. What would be the compound interest accrued on an amount of Rs. 8400 at the rate 12.5% per annum at the end 3 yr? (Rounded, off to two digits after decimal)

A. Rs. 420.62

B. Rs. 2584.16

C. Rs. 3560.16

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D. Rs. 3820.14

E. None of these

165. Twice the speed of a boat downstream is equal to thrice the speed upstream. The ratio of its speed in still water to the speed of current is

A. 1 : 5

B. 1 : 3

C. 5 : 1

D. 2 : 3

Explanation :

Let the boat speed in still water be b.

Let the stream speed be x.

2(b+ x) = 3(b-x)

5x=b

b/x=5/1

166. How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively, and the sum of terms is 40?

A. 15

B. 10

C. 5

D. 20

Explanation :

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Now the common difference of this AP is 16/4 = 4.

The sum of an AP is n/2 {2a + (n – 1)d}

Substituting we get, 40 = n/2 {2×-14 + (n – 1)4}

The best way to solve this is by plugging options. Put in n = 10 and get the RHS as 40.

167. A bottle is full of Dettol. One-third of it is taken out and then an equal amount of water is poured into the bottle to fill it. This operation is done four times. Find the final ratio of dettol and water in the bottle.

A. 13 : 55

B. 20 : 74

C. 16 : 65

D. 10 : 48

Explanation :

As in denominator we have to take 1/3 four times so, we start by assuming 81 ml of dettol in the bottle. After the first iteration you will be left with 2/3 × 81 = 54 ml. After the second iteration you will be left with 2/3 × 54 = 36 ml. After the third iteration you will be left with 2/3 × 36 = 24 ml. After the fourth iteration you will be left with 2/3 × 24 = 16 ml. So the required ratio will be 16 : (81 – 16) = 16 : 65

168. 7 cannibals of XYZ island, decide to throw a party. As you may be aware, cannibals are guys who eat human beings. The senior among them – Father Cannibal decides that any 6 of them will eat up one cannibal, then out of the remaining six – five of them will eat up one cannibal and so on till one is left. What is the time until one cannibal is left, if it takes one cannibal 3 hours to eat up one cannibal independently?

A. 7 hrs 11 min

B. 6 hrs 12 min

C. 7 hrs 21 min

D. 18 hrs 16 min

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Explanation :

At the beginning 6 cannibals will eat one, so time required will be 180/6 = 30 min.

Then out of the remaining six – five will devour one, so time required will be 180/5 = 36 min.

Thus the time until one cannibal is left will be = (180/6 + 180/5 + 180/4 + 180/3 + 180/2 + 180/1) min

= (30 + 36 + 45 + 60 + 90 + 180) min

= 441 min

= 7 hrs 21 min

169. Three articles are purchased for Rs. 1050, each with a different cost. The first article was sold at a loss of 20%, the second at 1/3rd gain and the third at 60% gain. Later he found that their SPs were same. What was his net gain/loss?

A. 14.28% gain

B. 13% loss

C. 12% loss

D. 11.11% gain

Explanation :

Let us assume that their CPs are x, y & z respectively.

According to the given condition 0.8x = 1.33y = 1.6z

⇒ (80/100)x = 400y/(3 × 100) = (160/100)z

⇒ x : y = 5 : 3 & y : z = 6 : 5

Thus x : y : z = 10 : 6 : 5

Hence CPs of the articles are x = (10/21) × 1050 = 500,

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y = (6/21) × 1050 = 300 &

z = (5/21) × 1050 = 250.

SP of the article with CP Rs. x is 0.8x = 0.8 × 500 = 400.

Since SPs are same, the total SP will be 400 × 3 = 1200.

Hence the gain % = (SP – CP)/CP × 100 = (1200 – 1050)/1050 × 100 = 14.28%.

170. In a game of tennis, A gives B 21 points and gives C 25 points. B gives C 10 points. How many points make the game?

A. 50 points

B. 45 points

C. 35 points

D. 30 points

171. A square, S1, circumscribes the circum circle of an equilateral triangle of side 10 cm. A square, S2, is inscribed in the in circle of the triangle. What is the ratio of the area of S1 to the area of S2?

A. 4:1

B. 32:1

C. 8:1

D. 2:1

Explanation :

The height of the equilateral triangle is 5√3 cm.

Since the height is also the median, we know that the circum-radius is 2/3 × 5√3 = 103/3 and the in-radius is 1/3 × 5√3 = 5√3/3.

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The diameter of the circumcircle is the side of square S1. So the area of S1 is (2 × 103/3)2 = 1200/9.

The diameter of the in-circle is the diagonal of square S2. So the area of S2 is ½ × (2 × 5√3/3)2 = 300/18.

Thus the ratio of areas S1 : S2 is 1200/9 : 300/18 = 8 : 1.

172. Three casks of equal capacities contain three liquids A, B & C in the ratio 1 : 2 : 3, 3 : 4 : 5 & 5 : 6 : 7 respectively. The mixtures from these casks are taken in the ratio 1 : 2 : 3 and poured into a 4th cask with the same capacity as that of the three casks and the cask is completely filled. What is the ratio of the liquids A, B and C in the resulting mixture?

A. 25:36:47

B. 16:21:26

C. 3:4:5

D. 1:2:3

Explanation :

⇒(1 + 2 + 3) = 6, (3 + 4 + 5) = 12 & (5 + 6 + 7) = 18. Common multiple of (6, 12, 18) = 36. So let us fix the capacities of the four casks as 36 litres each.

Liquid A Liquid B Liquid C

Cask 1 (36 liters) 6 12 18

Cask 2 (36 liters) 9 12 15

Cask 3 (36 liters) 10 12 14

Since the mixtures are taken in the ratio 1:2:3, 6litres, 12 litres and 18 litres mixture are drawn from the three casks respectively.

Liquid A Liquid B Liquid C

Cask 1 (6 liters) 1 2 3

Cask 2 (12 liters) 3 4 5

Cask 3 (18 liters) 5 6 7

Cask 3 (36 liters) 9 12 15

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Hence the ratio of the liquids in the resulting mixture is 9 : 12 : 15 = 3 : 4 : 5

173. A 30% loss on cost price is what percent loss on selling price?

A. 30%

B. 20%

C. 15%

D. None of these

Explanation :

Let CP = 100 ; SP=70

Loss= 30/70 × 100 = 42.85%

174. A, B and C hire a taxi for Rs. 2400 for one day. A, B and C used the car for 6 hours, 8 hours and 10 hours respectively. How much did C pay?

A. Rs. 800

B. Rs. 1000

C. Rs. 600

D. Rs. 1200

Explanation :

Let total fair be = 2400 ;

Therefore c share =10/24 × 2400 = 1000

175. The ratio of investments of A and B is 8 : 7 and the ratio of their yearend profits is 20 : 21. If B invested for 12 months, then find the period of investment of A:

A. 6 months

B. 8 months

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C. 10 months

D. 12 months

Explanation :

Let A invest for x months ; A = 8x months,

B = 7 × 12 = 84 months

8x/84 = 20/21

⇒ x = 10

176. What percent is 2 minutes 24 seconds of an hour?

A. 6%

B. 2%

C. 4%

D. 8%

Explanation :

%=144/60×60 = 4%

177. Evaluate: 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

A. 1

B. 3

C. 2

D. 5

Explanation :

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3 cos 80°. Cosec 10° + 2 cos 59° . cosec 31°

= 3 cos (90° - 10°). Cosec 10° + 2 cos (90° - 31°).Cosec 31°

=3sin10°.Cosec10° +2sin31°.cosec31°

=3+2=5

178. The total cost of 8 buckets and 5 mugs is Rs. 92 and the total cost of 5 buckets and 8 mugs is Rs. 77. Find the cost of 2 mugs and 3 buckets.

A. Rs. 35

B. Rs. 70

C. Rs. 30

D. Rs. 38

Explanation :

CP of 1 bucket = Rs. X

CP of 1 mug = Rs. Y

∴ 8x + 5y = 92....... (i)

5x + 8y = 77........(ii)

By equation (i) × 5 – equation (ii) × 8.

40x + 25y – 40x – 64y

= 460 – 616 ⇒ − 39y = - 156⇒ y = 4

From equation (i),

8x + 20 = 92 ⇒8x = 92 – 20 = 72 ⇒ x = 9

∴ CP of 2 mugs and 3 buckets

= 2 × 4 + 3 × 9 = 8 + 27 = Rs. 35

179. If 4x/3 + 2P = 12 for what value of P, x = 6?

A. 6

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B. 4

C. 2

D. 1

Explanation :

When x = 6, (4 * 6)/3 + 2P = 12

⇒ 8 + 2P = 12

⇒ 2P = 12 – 8 = 4

⇒ P = 2

179. The straight line 2x + 3y = 12 passes through:

A. 1st, 2nd and 3rd quadrant

B. 1st, 2nd and 4th quadrant

C. 2nd, 3rd and 4th quadrant

D. 1st, 3rd and 4th quadrant

Explanation :

The usual way to solve these type of questions is to put x = 0 once and find y coordinate. This would represent the point where the line cuts the Y axis.

Similarly put y = 0 once and find x coordinate. This would represent the point where the line cuts the X axis. Then join these points and you will get the graph of the line.

So when we put x = 0 we get y = 4.

When we put y = 0 we get x = 6.

So when we join these points we see that we get a line in 1st quadrant, which when extended both sides would go to 4th and 2nd quadrants. So option B.

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180. In ΔABC, ∠A + ∠B = 65°, ∠B + ∠C = 140°, then find ∠B.

A. 40°

B. 25°

C. 35°

D. 20°

Explanation :

∠A + ∠B = 65°

∴ ∠C = 180° - 65° = 115°

∠B + ∠C = 140°

∴ ∠B = 140° - 115° = 25°

181. The retail price of a water geyser is Rs. 1,265. If the manufacturer gains 10 %, the wholesale dealer gains 15 % and the retailer gains 25 %, then the cost of the product is:

A. 800

B. 900

C. 700

D. 600

Explanation :

C.P = 1265*100*100*100/110/115/125

C.P = 800

182. What percent of selling price would be 34 % of cost price if gross profit is 26 % of the selling price?

A. 17.16

B. 74

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C. 25.16

D. 88.40

Explanation :

X% of SP = 34% of CP

Also, P = 26% of SP

SP - CP = 0.26(SP)

CP = 0.74(SP)

Now, (34/100)×74

X = 25.16

183. The tax on a commodity is diminished by 10 % and its consumption increased by 10 %. The effect on the revenue derived from it changes by K %. Find the value of K.

A. 1.

B. -2

C. -1

D. 2

Explanation :

Directly using the formula, when a value is increased by R% and then decreased by R%, then net there is ( R∧2)/100 decrease. Putting R = 10, we get 1% decrease.

184. Ratio of Ashok's age to Pradeep's age is 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now?

A. 18

B. 21

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C. 15

D. 24

Explanation :

Given A/p= 4/3 Also A = 26 after 6 years, so his present age = 20years, Substituting we get P = 15 years.

185. The incomes of Chanda and Kim are in the ratio 9 : 4 and their expenditures are in the ratio 7 : 3. If each saves Rs. 2,000, then Chanda's expenditure is

A. 60000

B. 80000

C. 70000

D. None of these

Explanation :

Let the incomes of Chanda and Kim be 9x and expenditures be 7y and 3y respectively. Since = Income – Expenditure, we get 9x – 7y = 2000 and 4x – 3y = 2000. Solving, we get, x = 8000 and y = 10000. So Chanda’s expenditure = 7y = 7 × 10000 = Rs. 70,000.

186. A student purchased a computer system and a colour printer. If he sold the computer system at 10 % loss and the colour printer at 20 % gain, he would not lose anything. But if he sells the computer system at 5 % gain and the colour printer at 15 % loss, he would lose Rs. 800 in the bargain. How much did he pay for the colour printer?

A. 8000

B. 16000

C. 9000

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D. 533 4

Explanation :

Let C and P be the cost price of Computer and Printer respectively.

So CP = C + P, Case I,

SP = 0.9C + 1.2P.

Since he did not lose anything C + P = 0.9C + 1.2P C = 2P.

Case II, SP = 1.05C + 0.85P

Since there was the loss of Rs. 800

Rs.800 = C + P – 1.05C – 0.85P 80000 = 15P – 5C

Using equation from Case I, we get P = Rs.16000.

187. X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After 3 months X withdrew 2/7 of his stock but after 3 months, he puts back 3/5 of what he had withdrawn. The profit at the end of the year is Rs. 726. How much of this should X receive?

A. 336

B. 366

C. 633

D. 663

Explanation :

X’s profit : Y’s profit

= 700 × 3 + 500 × 3 + 620 × 6 : 600 × 12

= 2,100 + 1,500 + 3,720 : 7,200

= 7,320 : 7,200

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= 61 : 60

X’s share in the profit = 61/(60+61) × 726 = 366

188. A man sitting in a train travelling at the rate of 50 km/hr observes that it takes 9 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5 m long, find its speed.

A. 25

B. 45

C. 35

D. 36

Explanation :

Let required speed be x.

So,187.5/{ (x+50)*5/18} =9

189. A runs 5/3 times as fast as B. If A gives B a start of 80m, how far must the winning post be, so that A and B might reach it at the same time?

A. 200

B. 300

C. 270

D. 160

Explanation :

Ratio of speeds of A : B = 5 : 3, So If A runs 5, B runs 3. So difference in distance = 2. So if difference is 2, winning post is 5m. Hence if difference is 2.5*80, winning post is Hence 1st option.

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190. A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job?

A. 8

B. 9

C. 10

D. 12

Explanation :

Days taken in the general scenario = 360/N;

Days taken when 4 articles are prepared extra per day = 360/N + 4;

The difference in the day is one, therefore;

360/n - 360/n+4 =1

N2 + 4N – 1440 = 0;

N = 36, i.e. number of item prepared in general scenario is 36, and where 4 articles prepared extra is 40. Therefore no of days taken to complete the job = 360/40 = 9.

191. What is the equation of the line parallel to the line 2x + 3y = 12?

A. 2.4x + 1.8y = 16

B. 3.4x + 5.1y = 8

C. 4.2x + 3.3y = 18

D. 13.2x + 4.8y = 24

Explanation :

Slope of the given line is (-2/3). So, slope of the line parallel to it should be the same.

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As only in option 2, (-3.4/5.1) = -2/3 while the other equations do not have same slope.

Thus option 2 is the answer

192. What is the difference between cost price and the marked price of an article, sold at a loss of 11% for Rs. 2136 with a discount of 20%?

A. Rs. 178

B. Rs. 267

C. Rs. 240

D. Rs. 270

Explanation :

M.P. = 2136 /0.8 = Rs 2670 & C.P= 2136/0.89 = Rs 2400.

So required difference = 2670 – 2400 = Rs 270.

193. A gives B a start of 200m and still wins a km race by 200m. B gives a start of 100m and still wins by 100m in another km race with C. How much start should A give C in a km race in order to beat him by 250m?

A. 270

B. 480

C. 520

D. 230

Explanation :

Ratio of distance travelled by A and B ⇒ A : B = 1000 : 600, while that of B and C ⇒ B : C = 1000 : 800

Therefore, A : C = 1000 : 480.

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Since A beats him by 250m therefore C should be 750m away from the starting point.

So, A should give C a start of (750-480) = 270m in a km race in order to beat him

194. The simple interest accumulated in 4 years, with interest, R% p.a, on a particular sum is half of its principal. Find R.

A. 20%

B. 6%

C. 12.5%

D. 8.33%

Explanation :

S.I. = P*R*T/100 ⇒ P/2 = P*R*4/100 ⇒ R = 12.5%

195. If two dices are rolled simultaneously, then what is the probability of getting the sum of the numbers a prime number?

A. 14/36

B. 5/17

C. 15/29

D. 5/12

Explanation :

Prime no.s = 2, 3, 5, 7 & 11. The no of ways to get :

2 as the sum is 1 i.e. 1 +1

3 as the sum are 2 i.e. 1 + 2, 2 + 1

5 as the sum are 4 i.e. 1 + 4, 4 + 1, 2 + 3, 3 + 2

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7 as the sum are 6 i.e. 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3

11 as the sum are 2 i.e. 5 + 6, 6 + 5

So total no of ways are 1 + 2 + 4 + 6 + 2 = 15

So the probability is 15 / 36 = 5 / 12 (where 36 is total number of possible cases in case of two dices)

196. A multiplex owner increases the price of a ticket by 25%, because of which the number of viewers decrease by 25%. What is the percentage change in the revenue?

A. 6.25% increase

B. 9.375% increase

C. 6.25% decrease

D. 9.375% decrease

Explanation :

Using the formula a + b + ab/100, we get 25 - 25 - (625/100) i.e. -6.25.

So there is decrease of 6.25% in revenue.

197. A and B start a business by investing 5 lks and 4 lks. B remains in the business for a complete year. How long did A remain in the business, if they received equal profit at the end of the year?

A. 9.6 months

B. 2.4 months

C. 8.4 months

D. 6.9 months

Explanation :

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Let N be the time period of A. Since the profits are equal, we get 4 x 12 = 5 x N,

On solving, we get N = 0.8 year or 9.6 months

198. What is the remainder when addition of all the 2-digit multiples of 9 is divided by 11?

A. 0

B. 1

C. 2

D. 3

Explanation :

Two digit multiples of 9 are 18, 27, ......, 99 which are 10 in number.

By A.P. formula we can find the addition of 2 digit multiples of 9.

Sum = [10/2(18+99)] = 585. So 585/11, we get remainder as 2.

199. 60% of the students learn German and 50% of the students learn French. If student in the class learns at least one subject out of the given two, then what percent of the students do not learn both the subjects?

A. 10

B. 12

C. 80

D. 90

Explanation :

8. Total percentage of both german and english = 50+60 = 110%. So 10% learn both

Therefore, 100-10 = 90% do not learn both.

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200. In the inequality, x2 - 14x + 50 < 5, find the range of x.

A. 5 > x > 9

B. 5 < x < 9

C. -5 < x < 9

D. -5 > x > -9

Explanation :

x2 - 14x + 50 < 5 ⇒ (x-9)(x-5)<0

Now, here 2 cases arises

Case 1: (x-9)<0 & (x-5)>0

So we get range to be 5 < x < 9

Case 2: (x-9)>0 & (x-5)<0

Which gives x > 9 and x < 5 which cannot occur simultaneously, hence rejected.

201. Percent profit earned when an article is sold for Rs. 546/- is double the percent profit earned when the same article is sold for Rs. 483/-. If the marked price of the article is 40% above the cost price, what is the marked price of the article?

A. Rs. 588/-

B. Rs. 608/-

C. Rs. 616/-

D. Rs. 596/-

E. Rs. 586/-

Explanation :

Let profit be P and C.P.= x

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Now, x+2P=546

x+P=483

subtracting both,

P=63

x=483-63=420

M.P.= 1.4*420=588

202. A vessel contains 180 litres of mixture of milk and water in the respective ratio of 13 : 5. Fifty-four litres of this mixture was taken out and replaced with 6 litres of water, what is the approximate percentage of water in the resultant mixture?

A. 41

B. 31

C. 24

D. 9

E. 17

Explanation :

Milk: water = 13:5

Volume of solution=180 l

Solution taken out= 54 l

Volume of solution left= 180-54=126 l

In 126 l solution,

Milk= 126*13/18= 91 l

Water=126*5/18=35 l

As 6 l water is added

Water= 35+6= 41 l

Total solution volume= 126+6= 132 l

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Percentage of water= 41/132*100= 31%

203. The average age of all the 100 employees in an office is 29 years, where 2/5 employees are ladies and the ratio of average age of men to women is 5 : 7. The average age of female employees is:

A. 18 years

B. 35 years

C. 25 years

D. 30 years

E. None of these

Explanation :

Total no. of employees =100

No. of females= 2/5 of 100= 40

No. of males = 60.

Avg. of employee= 29

Sum of ages of all the employees= 29×100= 2900

ratio of average age of men to women is 5 : 7

Let the avr of men = 5X and avg of women =7X

5X ×60+ 7X×40 =2900

X=5

Average age of female employees= 5 ×7=35

204. A man sets out on cycle from Delhi to Faridabad, and at the same time another man starts from Faridabad on cycle for Delhi. After passing each other they complete their journeys in 2 6 7 and 5 3 5 hours respectively. At what rate does the second man cycles if the first man cycles at 14 kmph?

A. 10 kmph

B. 5 kmph

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C. 7 kmph

D. 8 kmph

E. None of these

Explanation :

Speed1/speed2 = √time2/√time1

14 km/h/speed2 = √535/√267

We get Speed2 =√97.81 = 9.88 km/h

DIRECTIONS for question 5 to 7: What approximate value will come in place of question mark (?) in the given question? (You are not expected to calculate the exact value)

205. A number is such that when it is multiplied by ‘8’, it gives another number which is as much more than 153 as the original number itself is less than 153. What is 25% of the original number?

A. 8

B. 10

C. 8.5

D. 6.5

E. 9

Explanation :

Let the no. be X

Given 8X-153=153-X

Hence X=34

25% of X=8.5

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206. The HCF and LCM of two num¬bers are 12 and 924 respectively. Then the number of such pairs is

A. 0

B. 1

C. 2

D. 3

E. 4

Explanation :

Let the numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

⇒ xy = 77

∴ Possible pairs = (1, 77) and (7,11)

207. By walking at 3/4 of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is

A. 75 minutes

B. 60 minutes

C. 40 minutes

D. 30 minutes

E. 20 minutes

Explanation :

4/3 of usual time = Usual time + 20 minutes

1/3 of usual time

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= 20 minutes

Usual time = 20 × 3 = 60 minutes

208. A man sells two pipes at Rs. 12 each. He gains 20% on one and loses 20% on the other. In the whole transaction, there is

A. neither loss nor gain

B. Profit of Rs. 1

C. Loss of Rs. 1

D. profit of Rs. 2

E. None of these

Explanation :

S.P of each pipe = Rs 12

One is sell at 20% i:e 120%of C.P =12

C.P of 1st pipe= Rs 10

Other is sold at loss of 20% i:e 80% of C.P of 2nd pipe = Rs 12

So C.P of 2nd pipe = Rs 15

Total C.P = Rs 25

Total S.P = Rs 24

Net profit = Rs 1

209. C is 20% more efficient than A. A and B together can finish a piece of work in 16 days. B and C together can do it in 15 days. In how many days A alone can finish the same piece of work?

A. 42

B. 48

C. 54

D. 36

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E. 45

Explanation :

Let total of 240 units of work to be done.

Now as given A+ B can do 240/16= 15 units/day

Also B+C can do 240/15= 16 units/day

And given, C= 1.2 A., Substituting and solving the equations we get, A= 5 units/day, ie.e A will complete work in 240/5= 48 days

210. A started a business with an investment of Rs. 16,000. After 6 months from the start of the business, B and C joined with Rs. 12,000 and Rs. 18,000 respectively and A invested an additional amount of Rs. 4000. If the difference between A’s share and B’s share in the annual profit is Rs. 6000, what was the annual profit received?

A. Rs. 17,600

B. Rs. 13,200

C. Rs. 14,300

D. Rs. 16,500

E. Rs. 11,000

Explanation :

Amount invested by A= 16000 for first 6months, and 20000 for next 6 months

Amount invested by B= 12000 for 6 months

Amount invested by C= 18000 for 6 months

Now by compound partnership, IA:IB:IC = PA : PB : PC

16000*6 + 20000*6 : 12000*6 : 18000*6 = 6:2:3

Given 6x – 2x= 4x = 6000; x=1500

so total profit = 11x = 16500.

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211. Type A, 12 kg of rice worth Rs. 40/kg is mixed with Type B, rice worth Rs. 24/kg. What should be the quantity of Type B rice, if the mixture is sold at Rs. 45/kg with 25% profit added in it?

A. 18

B. 48

C. 4

D. Can’t Say

Explanation :

C.P. of the mixture = 45/1.25 = Rs. 36/kg..

So, (40-36)/(36-24) = (N)/(12) ⇒ N = 4 Kg.

212. A person spends 1/7th of his salary on travel,1/3rd of the remaining on food, he then spends 1/4th of the remaining on rent. Finally he puts 1/6th of the remaining as a monthly savings, after which he has 25000 left. What is his salary (in Rs.)?

A. 70 K

B. 14 K

C. 84 K

D. 26 K

Explanation :

Let M be the total salary

Therefore, as per question, M × (6/7) × (2/3) × (3/4) × (5/6) = Rs 25000

M = Rs 70000

213. Point C(x,y) divides the distance AB with point A(8,12) and point B(16, 18) in a ratio of 3:5, with AC being shorter than BC. What are the co-ordinates of C?

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A. (12,15)

B. (14.5, 12.5)

C. (11,14.25)

D. (8.3, 45)

Explanation :

x co-ordinate of C = [(5×8) + (3×16)] / (3+5) = 11

y co-ordinate of C = [(5×12) + (3×18)] / (3+5) = 14.25

Co-ordinates of C is ( 11, 14.25 )

214. How many terms of the sequence -12, -8, -4,…so on, to make a sum of 120?

A. 11

B. 12

C. 10

D. 13

Explanation :

The series is in A.P. where a = -12 and d = 4.

So 120 = (n/2)[2 × (-12) + (n -1) × 4].

On solving this, we get n = 12

215. A TV set listed at Rs 3200 is sold to a retailer at a successive discount of 25% and 15%. The retailer desires a profit of 20%, after allowing a discount of 10% to the customer. At what price should he list the TV set (in Rs.)?

A. 2720

B. 2448

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C. 2448

D. 2133

Explanation :

The retailers C.P. = 3200 × 0.75 × 0.85 = Rs 2040.

His expected S.P. = 2040 × 1.2 = Rs 2448.

But S.P. is 90% of the L.P., as there is a discount of 10%.

So L.P. = 2448/0.9 = Rs 2720

216. What is the average of the first 100 odd natural numbers?

A. 100.5

B. 125

C. 50

D. 100

Explanation :

As we know, sum of first n odd numbers is n2

Therefore, sum of 1st 100 odd numbers is 1002 and average will be 1002/100 = 100.

217. A, B and C invested capitals in the ratio 2 : 3 : 5, the timing of their investment being in the ratio 9 : 5 : 6. The profit if any will be distributed in the ratio

A. 1:2:3

B. 11:8:11

C. 7:2;1

D. 6:5:10

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Explanation :

Ratio of capitals = 2 : 3 : 5 and that of time = 9 :5: 6

Therefore, ratio of profits = 2 × 9 : 3 × 5 : 5 × 6 = 18 : 15 : 30 or 6 : 5 : 10

218. It takes 5 sec. for a clock to strike at 5’o clock. If the striking intervals are uniform how much time will it take to strike 9’o clock (in sec.)?

A. 9

B. 10

C. 11

D. 12

Explanation :

There are 4 intervals in 5 strokes.

Time taken to strike 1 stroke will be 5/4 sec.

At 9, there will be 9 strokes and 8 intervals between two strokes.

Thus time required = 5/4 × 8 = 10 sec

219. From the top of the Tower which is 240m high, if the angle of depression of a point on the ground is 30°, then the distance of the point from the foot of the Tower is <

A. 40√3

B. 80√3

C. 120√3

D. 240√3

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Explanation :

220. Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:

A. 8 cms

B. 12 cms

C. 14 cms

D. 16 cms

221. If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be :

A. 128

B. 132

C. 133

D. 136

Explanation :

If values are proportional to 13 : 11 : 7, then the number of coins will be proportional to 13/1 : 11/0.50 : 7/0.25 ⇒ 13 : 22 : 28. Now from this the number of coins of 50 paise will be 378 × 22/63 = 132.

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222. A person travels 48 kms at 12 kms/hour and further 48 kms at 16km.s/hour. His average speed for the whole

A. 14 km/hour

B. 13(4/7)km/hour

C. 12(5/7)km/hour

D. 13(5/7)km/hour

Explanation :

Avg. Speed = (Total Distance / Total Time)

TD = 48 + 48= 96,

T1 = 48/12 = 4hrs

T2 = 48/16 = 3hrs

T1 + T2 = 4 + 3 = 7

Avg Speed = 96/7 = 13(5/7) km/hr

4. Simplify (0.001344 / 0.3 x 0.7) = ?

A. 0.0064

B. 0.064

C. 0.64

D. 6.4

Explanation :

(0.001344 / 0.3 x 0.7) = 0.0064

223. The difference of two numbers is 11 and one fifth of their sum is 9. The numbers are :

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A. 31, 20

B. 30, 19

C. 29, 18

D. 28, 17

Explanation :

x − y = 11, x + y = 5 × 9 x − y = 11, x + y = 45, y = 17, x = 28

224. How many numbers between 1 and 100 are divisible by 7 ?

A. 9

B. 11

C. 17

D. 14

Explanation :

No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d

98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7

98/7= N = 14

225. What is the number which when multiplied by 13 is increased by 180?

A. 13

B. 15

C. 23

D. 35

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Explanation :

13 × 15 = 195

226. In 24 minutes, the hour hand of a clock moves through an angle of:

A. 60°

B. 24°

C. 12°

D. 5°

Explanation :

12 hour = 360°, 1 hr. = 360/12 = 30° 60 min = 30°, 1 min 30/60 = .5° 24 min. = 1/2 ×24 = 12°

227. √0.0081 is equal to :

A. 0.09

B. 0.9

C. ±0.08

D. 0.81

Explanation :

√0.0081 = √0.0081/10000 = √81/10000 = 9/100 =0.09

228. A reduction of 20% in the price of mangoes enables a person to purchase 12 more for Rs. 15. What was the price of 16 mangoes before reduction of price ?

A. Rs. 6

B. Rs. 5

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C. Rs.7

D. Rs. 9

Explanation :

Price x Consumption = Expenditure

Consumption = Exp. Price

(15 / 8x) - (15 / x) = 12

x = (15 x 2) / (12 x 8)

For 16 Mangoes = [(15 x 2) / (12 x 8)] x 16 = 5

229. Dharma invested Rs. P for 3 years in scheme A which offered 12% p.a. simple interest. She also invested Rs. P + 400 in scheme B which offered 10% compound interest (compounded annually), for 2 years. If the amount received from scheme A was less than that received from scheme B, by Rs. 304, what is the value of P?

A. Rs. 1400

B. Rs. 1000

C. Rs. 1500

D. Rs. 900

E. Rs. 1200

Explanation :

As given, P + 3*12*P/100 + 304 = (P+400)(1+11/100)2

P(0.15)= 180;

P= 1200

230. Shiva gives 20% of her monthly salary to his mother, 50% of the remaining salary he invests in an insurance scheme and PPF in the respective ratio of 5 : 3 and the remaining he keeps in his bank account. If the sum of the

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amount he gives to his mother and that he invests in PPF is Rs. 12,600, how much is Shiva’s monthly salary?

A. Rs. 36,000

B. Rs. 64,000

C. Rs. 42,000

D. Rs. 40,000

E. None of these

Explanation :

Let the total amount be x.

0.2x = given to mother.

0.25x= invested in insurance

0.15x= invested in ppf

0.4x= Bank account

Given, 0.2x+0.15x = 0.35x = 12600; x=36000

231. The respective ratio of radii of two right circular cylinders (A & B) is 4 : 7. The respective ratio of the heights of cylinders A and B is 2 : 1. What is the respective ratio of volumes of cylinders A and B?

A. 25 :42

B. 23 : 42

C. 32 : 49

D. 30 : 49

E. 36 : 49

232. If 4x/3 + 2P = 12 for what value of P, x = 6?

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A. 6

B. 4

C. 2

D. 1

Explanation :

When x = 6, (4 * 6)/3 + 2P = 12

⇒ 8 + 2P = 12

⇒ 2P = 12 – 8 = 4

⇒ P = 2

233. In ΔABC, ∠A + ∠B = 65°, ∠B + ∠C = 140°, then find ∠B.

A. 40°

B. 25°

C. 35°

D. 20°

Explanation :

∠A + ∠B = 65°

∴ ∠C = 180° - 65° = 115°

∠B + ∠C = 140°

∴ ∠B = 140° - 115° = 25°

234. There are two motor cycles (A & B) of equal cost price. Motorcycle A was sold at a profit of 14% and motorcycle B was sold for Rs. 4,290/- more than its cost price. The net profit earned after selling both the motor cycles (A & B) is 20%. What is the cost price of each motorcycle?

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A. Rs. 16,500/-

B. Rs. 16,000/-

C. Rs. 15,500/-

D. Rs. 71,500/-

E. Rs. 17,000/-

Explanation :

Let the cost price of each motorcycle be Rs. ‘A’. So SP of A = 1.14A and SP of B = A + 4290. Total CP = 2A. As net profit is given to be 20% on both the motorcycles, so we can form the equation as (2.14A + 4290 - 2A)/2A = 20%. Solving it further, we get (0.14A + 4290)5 = 2A. Solving this equation, we get value of A as 16,500. Hence answer is option A

235. Raman invested Rs. P for 2 years in scheme A which offered 20% p.a. compound interest (compounded annually). He lent the interest earned from scheme A to Shubh, at the rate of 7.5% p.a. simple. If at the end of 2 years, Shubh gave Rs. 3036 to Raman and thereby repaid the whole amount(actual loan + interest), what is the value of P?

A. Rs. 6000

B. Rs. 5800

C. Rs. 6800

D. Rs. 5400

E. Rs. 6400

Explanation :

P*(1.2)2 = 1.44P

Interest = P – 1.44P = 0.44P

0.44P + (0.44P * 7.5 * 2)/100 = 3036

Solving, we get P = 6000.

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236. Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it is

A. 1/5

B. 1/3

C. 2/5

D. None of these

Explanation :

Joint probability of all not being able to solve it is

237. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 metres away from the tree the angle of elevation becomes 30°. The breadth of the river is

A. 40 m

B. 20 m

C. 30 m

D. 60 m

238. If A's income is 50% less than that of B's, then B's income is what per cent more than that of A?

A. 125

B. 100

C. 75

D. 50

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Explanation :

Required percentage

239. 1.14 expressed as a per cent of 1.9 is

A. 6%

B. 10%

C. 60%

D. 90%

Explanation :

Required percentage

240. Two natural numbers are in the ratio 3 : 5 and their product is 2160. The smaller of the numbers is

A. 36

B. 24

C. 18

D. 12

Explanation :

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241. If 60% of A = ¾ of B, then A : B is

A. 9 : 20

B. 20 : 9

C. 4 : 5

D. 5 : 4

Explanation :

242. Two successive price increases of 10% and 10% of an article are equivalent to a single price increase of

A. 19%

B. 20%

C. 21%

D. 22%

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Explanation :

Single equivalent percentage increase in price

243. If then x is equal to

A. 5/12

B. 12/5

C. 5/7

D. 7/5

Explanation :

244. An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm2) of this regular hexagon will be

A.

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B.

C.

D.

Explanation :

side of regular hexagon =1/3 *6 = 2 cm

Area of the hexagon = 3 √3/ 2 a2

= 3 √3/2 *2*2 =6 √3 sq.cm

245. A and B together can do a work in 10 days. B and C together can do the same work in 6 days. A and C together can do the work in 12 days. Then A, B and C to¬gether can do the work in

A. 28 days

B. 14 days

C. 5 5/7 days

D. 8 2/7 days

Explanation :

(A+B)' 1 day's work = 1/10

(B+C) 1 day's work = 1/6

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(C+ A) 1 day's work = 1/12

2(A+B+C)' 1 day's work

=1/10 + 1/6 + 1/12 = 6+10+5 / 60

=21/60 = 7/20

=>(A+B+C)' 1 day's work = 7/40

=>All three together will complete the work in 40/7 = 5 5/7days.

246. A does half as much work as B in three- fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it alone?

A. 30 days

B. 35 days

C. 40 days

D. 45 days

Explanation :

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247. If a wire is bent into the shape of a square, then the area of the square so formed is 81cm2. When the wire is rebent into a semicircular shape, then the area, (in cm2) of the semicircle will be (Take π = 22/7)

A. 22

B. 44

C. 77

D. 154

Explanation :

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248. In an examination hall, there are four rows of chairs. Each row has 8 chairs, one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that in each row all students belong to the same class should sit and that no two adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?

A. 2 x 16! x 16!

B. 2 x 16! x 15!

C. 2 x 15! x 15!

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D. 2 x 14! x 16!

Explanation :

Students can be adjusted in 16! x 16! ways.

Rows can be adjusted in 2 ways.

So the final answer will be the 1st option.

249. There are three events A, B and C, only one of which must happen. The odds are 8 to 3 against A, 5 to 2 against B. Find the odds against C.

A. 43 : 34

B. 43 : 77

C. 34 : 43

D. 77 : 43

Explanation :

P(A) = 3/11 & P(B) = 2/7 . So probability of happening of C = 1 – ( 3/11+ 2/7) = 34/77 . So the odds against C are 43:34.

250. 1,496 cm3 of a metal is used to cast a pipe of length 28 cm. If the internal radius of the pipe is 8 cm, the outer radius of the pipe is

A. 7 cm

B. 10 cm

C. 9 cm

D. 12 cm

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251. A man is standing on the 8 m long shadow of a 6 m long pole. If the length of the man’s shadow is 2.4 m, then the height of the man is

A. 1.4 m

B. 1.8 m

C. 1.6 m

D. 2.0 m

Explanation :

8 m shadow. Length of pole is = 6m.

2.4 m shadow will have = 6/8 x 2.4 = 1.8 m height of the man as answer.

252. In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is

A. 14 years 8 months

B. 16 years 4 months

C. 15 years

D. 17 years 10 months

Explanation :

Decrease of 20 x 2 = 40 months means that incoming boy has age 18 years – 40 months

= 14 years and 8 months.

253. Two taps can separately fill a cistern in 10 minutes and 15 minutes, respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in

A. 7 minutes

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B. 13 minutes

C. 9 minutes

D. 23 minutes

Explanation :

1/6 - 1/x = 1/18

Try option in place of x and get answer as third option.

254. A boatman goes 2 km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. How long will he take to go 5 km in stationary water?

A. 1 hour

B. 3/2 hours

C. 1 hour 15 minutes

D. 40 minutes

Explanation :

In 1 hr he goes 2 km against the stream and with the current he will go 6 km in 1 hr.

In still water he will go 4 km in 1 hr. So it will take 1.15 hr for 5 km.

255. A person travels 285 km in 6 hours in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hour. In the second part of the journey, he travels by train at the speed of 55 km per hour. How much distance did he travel by train?

A. 205 km

B. 165 km

C. 145 km

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D. 185 km

Explanation :

Just go by options. In 3 hours he will travel 165 by train and By bus 120 km in next the 3 hours.

So 2nd option.

256. If there are six periods in each working day of a school, in how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

A. 3500

B. 1800

C. 3600

D. 1750

Explanation :

Let us take a case where we have decided which specific subject has a double class.

Now we have 6 periods and we have filled all of them up – but with one subject being repeated.

These can be arranged in 6!/2! = 360 ways. Now any of the 5 subjects can be repeated.

So total no. of possibilities is – 360 x 5 = 1800.

257. A monument has 50 cylindrical pillars each of diameter 50 cm and height 4 m. What will be the labour charges for getting these pillars cleaned at the rate of 50 paise per sq. m? (Use π = 3.14)

A. Rs. 237

B. Rs. 157

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C. Rs. 257

D. Rs. 353

Explanation :

Direct formula putting

= 2 x π x r x h x 50 ÷ ( 2 x 100)

= 50 x 2 x 3.14 x 25 x 4 ÷ (2 x 100)

258. A mixture contains wine and water in the ratio 3 : 2 and another mixture contains them in the ratio 4: 5. How many liters of the latter must be mixed with 3litres of the former so that the resultant mixture may contain equal quantities of wine and water?

A. 1 2/3 litre

B. 2/5 litre

C. 3 3/4 litre

D. 4 1/2 litre

E. None of these

Explanation :

By applying allegation and mixture

So we got ratio of two mixture = 5:9

It means 5 unit = 3 liters

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We get 9 unit = 3/5 ×9 = 27/5 liters

259. A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total. If he sold one of the bullocks at a gain of 20%, the other is sold at a loss of

A. 20%

B. 18 2/9%

C. 14 2/7%

D. 21%

E. None of these

Explanation :

A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total.

As he sold one bullocks at a gain of 20%, it means 120% of C.P = 8400

We get C.P of one bullocks = 7000

So gains on one bullocks = Rs 1400

Other bullocks is sold at lose and there is neither losing nor gaining in total

So loss on 2nd bullocks = 1400/7000×100 =20%

260. Two trains, A and B, start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet if train A is moving at 45 km/hr., then the speed of the train B is

A. 60 km/hr

B. 64.8 km/hr

C. 54 km/hr

D. 37.5 km/hr

E. None of these

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Explanation :

Speed1 : Speed2 = √Time2 : √Time1

45km/h :speed2 = √10/3 : √24/5

We get speed2 = 54km/hr

261. Out of his total income, Mr. Kapoor spends 20% on house rent and 70% of the rest on house hold expenses. If he saves Rs 1,800 what is his total income (in rupees)?

A. Rs 7,800

B. Rs 7,000

C. Rs 8,000

D. Rs 7,500

E. None of these

Explanation :

Let the total income of Mr. Kapoor be 100 units.

As Mr. Kapoor spends 20% on house rent and 70% of the rest on house hold expenses.

So he spends 76% of his income.

It means 24 unit income = Rs 1,800

Total income = 1,800/24 ×100 = Rs. 7500

262. A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?

A. 7 days

B. 7 2/3 days

C. 7 1/3 days

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D. 8 days

E. None of these

Explanation :

A can do a piece of work in 8days which B can destroy in 3 days.

So let the total work be 24 units.

So unit contributed by A and B in one day is 3 units and -8 units respectively .

A has worked for 6 days, during the last 2 days of which B has been destroying.

So total units completed in 6 days = 6×3 + 2× (-8) = 2 units.

So remaining 22 units is done by A alone with efficiency of 3 units per day.

So number of days required to complete the work = 22/3 days

263. A garrison of 750 men has provisions for 20 weeks. If at the end of 4 weeks, they are re-inforced by 450 men, how long will the provision last?

A. 8 weeks

B. 12 weeks

C. 14 weeks

D. 15 weeks

E. 10 weeks

Explanation :

750 * 20 = 750 * 4 + 1200 * W => W = 10 weeks

264. Bill, Simon, and John are brothers, given Simon is the eldest. Bill is as many years younger than one brother as he is older than the other. Simon is 7 years younger than twice the age of John. John is 5 years older than half the age of Bill. What is the sum of the ages of Bill, Simon and John?

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A. 12

B. 24

C. 48

D. Can’t say

Explanation :

S – B = B – J J = B/2 + 5. S = 2J – 7.

S = B + 10 – 7 = B + 3.

J = + 5. 2S = B + 10. + 5 + B + 3 = 2B. = 8. B = 16, S = 19, J = 13. So B + S + J = 16 + 19 + 13 =48.

265. The cost price of item B is Rs. 150/- more than the cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?

A. Rs. 450/-

B. Rs. 420/-

C. Rs. 400/-

D. Rs. 350/-

E. Rs. 480/-

Explanation :

Let us assume cost price of A= X

So that Cost price of B= X+150.

SP of A= X*1.1

SP of B=(X+150)*0.8

Given that

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SPA: SPB

11:12

So that 1.1X/(X+150)*0.8= 11/12

X=300

CP of B= 300+150=450

266. The number of ways in which 7 boys and 8 girls can be seated in a row so that they are alternate

A. 203121800

B. 29030400

C. 3628800

D. 203212800

E. 3628800

Explanation :

Reqd. number of ways = 7! × 8! = 203212800.

267. There are 13 married couples, 5 single men and 7 single women in a party. Every man shakes hand with every woman once, but no one shakes hand with his wife. How many handshakes took place in the party?

A. 247

B. 347

C. 360

D. 191

E. 100

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Explanation :

Any single man will have = 13 + 7 = 20 options.

Total number of handshakes by single men = 20 × 5= 100. Any married man will have 12 + 7 = 19 options. Total number of handshakes by married men = 19 × 13 = 247. Total number = 247 + 100 = 347.

268. The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is

A. 0

B. 1

C. 2

D. 3

Explanation :

Let the numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

=> xy = 77

∴ Possible pairs = (1,77) and (7,11)

269. What is the least number which, when divided by 5, 6, 7, 8 gives the remainder 3 but is divisible by 9?

A. 1463

B. 1573

C. 1683

D. 1793

Explanation :

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LCM of 5, 6, 7, 8 = 35 × 24 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9.

For k = 2, it is divisible by 9.

∴ Required number = 840k + 3

= 840 × 2 + 3 = 1683

270. Three numbers are in the ratio 3:4: 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is

A. 20

B. 27

C. 39

D. 52

Explanation :

Let the numbers be 3x, 4x and 5x.

∴ 5x + 3x = 4x + 52

=> 4x = 52 => x =13

∴ The smallest number = 3x = 3 × 13 = 39

271. If the radius of a circle is increased by 50%, its area is increased by

A. 125%

B. 100%

C. 75%

D. 50%

Explanation :

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Percentage increase in area

272. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in

A. 10 2/3 days

B. 10 1/2 days

C. 10 1/4 days

D. 10 1/3 days

Explanation :

Part of work done by A and B in first two days

Part of work done in first 10 days = 35/36

Remaining work = 1 – 35/36 = 1/36

Now it is the turn of A.

∴ Time taken by A = 1/36 × 9 = ¼

∴ Total time = 10 + ¼ = 10 ¼ days

273. In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?

A. 12 years

B. 11 years

C. 10.5 years

D. 10 years

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Explanation :

Father + mother = 2 × 35 = 70 years

Father + mother + son = 27 × 3 = 81 years

Son’s age = 81 – 70 = 11 years

274. If 5 men or 7 women can earn Rs. 5,250 per day, how much would 7 men and 13 women earn per day?

A. Rs. 11,600

B. Rs. 11.700

C. Rs. 16,100

D. Rs. 17,100

Explanation :

5 men = 7 women

7 men

Mark Price = 140

7 men + 13 women

Now,

∵ 7 women = Rs. 5250

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275. If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?

A. 60

B. 45

C. 40

D. 30

Explanation :

(A + B)’s 1 day’s work =

B’s 1 day’s work =

A’s 1 day’s work =

A alone will do the work in 60 days.

276. By walking at 3/4 of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is

A. 75 minutes

B. 60 minutes

C. 40 minutes

D. 30 minutes

Explanation :

of usual time = Usual time + 20 minutes

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of usual time

= 20 minutes

Usual time = 20 × 3 = 60 minutes

277. 4.41*0.16/2.1*1.6* 0.21 is simplified to

A. 1

B. 0.1

C. 0.01

D. 10

Explanation :

278. The list price of an article is Rs. 160 and a customer buys it for Rs. 122.40 after two successive discounts. If the first discount is 10%, then second discount is

A. 12%

B. 10%

C. 14%

D. 15%

Explanation :

SP after a discount of 10%

= (160*90) / 100 = Rs. 144

Second discount

= 144 – 122.40 = Rs. 21.6

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If the second discount be x% then

279. In a school, 10% of number of girls is equal to 1/20 of number of boys. Ratio between the 'number of boys to number of girls is

A. 1:2

B. 2:1

C. 1:4

D. 4:1

Explanation :

LIf boys = x and girls = y, then

280. If a, b, c, d, e are five consecutive odd numbers, their average is

A. 5(a + 4)

B. abde/5

C. 5(a + b + c + d + e)

D. a + 4

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Explanation :

b = a + 2

c = b + 2 = a + 4

d = c + 2 = a + 6

e = d + 2 = a + 8

Therefore, Required average = (a + a + 2 + a + 4 + a + 6 + a + 8)/5

= a + 4

281. The average of 20 numbers is 15 and the average of first five is 12. The average of the rest is

A. 16

B. 15

C. 14

D. 13

Explanation :

If the average of remaining numbers be x, then

20 × 15 = 5 × 12 + 15x

⇒ 300 = 60 + 15x

⇒ 15x = 300 – 60 = 240

=> x = 240/15 = 16

282. A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article (in Rs.) was

A. 100

B. 200

C. 400

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D. 500

Explanation :

C. P. of article = Rs. X

∴ First SP = 80x/100 = Rs. 4x/5

Case II

⇒ 5x = 2000 ⇒ x = 2000/5 = Rs. 400

283. The price of an article is first decreased by20% and then increased by 30%. If the resulting price is Rs. 416, the original price of the article is

A. Rs. 350

B. Rs. 405

C. Rs. 400

D. Rs. 450

Explanation :

If the original price of article be Rs. X, then

284. A man performs 2/15 of the total journey by train 9/20 by bus and the remaining 10 km on foot. His total journey in km is

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A. 15.6

B. 24

C. 16.4

D. 12.8

Explanation :

If the total journey be x km, then

2x/15+9x/20+10=x

=>x-2x/15-9x/20=10

=> 60x-8x-27x/60=10

=> 25x/60=10

=> X=60*10/25=24km

285. By walking at 3/4 of his usual speed, a man reaches his office 20 minutes later than usual. His usual time is

A. 30 min

B. 75 min

C. 90 min.

D. 60 min.

Explanation :

New speed = 3/4 × usual speed

∴ New time = 4/3 × usual time.

∴ 1/3 × usual time = 20 minutes

⇒ Usual time = 3 × 20

= 60 minutes

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286. If the compound interest on a certain sum for two years at 12% per annum is Rs. 2544 the simple interest on it at the same rate for 2 years will be

A. Rs. 2400

B. Rs. 2500

C. Rs. 2480

D. Rs. 2440

Explanation :

287. The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 275, then the mean profit for the last 15 days would be

A. Rs. 200

B. Rs. 350

C. Rs. 275

D. Rs. 425

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Explanation :

Average would be : 350 = (275 + x)/2

On solving, x = 425.

288. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.

A. Rs. 480

B. Rs. 520

C. Rs. 420

D. Rs. 460

Explanation :

Let d be the average daily expenditure

Original expenditure = 35 × d

New expenditure = 35 × d + 42

New average expenditure will be :

(35 × d + 42)/42 = d - 1

On solving, we get d = 12

Therefore original expenditure = 35 × 12 = 420

289. The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day Rs. 1,325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?

A. Rs. 750

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B. Rs. 1000

C. Rs. 850

D. Rs. 1250

Explanation :

Let x be the number of passengers and y be the fare taken from passengers.

3xy + 50xy = 1325 => xy = 25

Amount collected from II class passengers = 25 × 50 = Rs. 1250.

290. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/hour and the speed of the current is 3 km/hour, the distance between A and B is

A. 4 km

B. 8 km

C. 6 km

D. 12 km

Explanation :

Let d be the distance between A and B

So, d/12 + d/6 = 3 d = 12 km

291. A man while returning from his factory, travels 2/3 of the distance by bus, ¾ of the rest partly by car and partly by foot. If he travels 2 km on foot, find the distance covered by him.

A. 24 km

B. 22 km

C. 28 km

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D. 26 km

Explanation :

Therefore D = 24 km

292. The fuel indicator in a car shows 1/5th of the fuel tank as full. When 22 more liters of fuel are poured in to the tank, the indicator rests at the 3/4of the full mark. Find the capacity of the tank.

A. 25 litres

B. 35 litres

C. 30 litres

D. 40 litres

Explanation :

x/5 + 22 = 3x/4 ⇒ x = 40 litres

293. A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m3. The emptying capacity of the pump is 10m3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.

A. 45 m3/min

B. 40 m3/min

C. 50 m3/min

D. 55 m3/min

Explanation :

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(2400/x) - (2400/(x + 10)) = 8, Solving this we get x

= 50m3/min

Or by options (2400/50) - (2400/60) = 48 - 40 = 8 minutes

294. A sum of money is accumulating at compound interest at a certain rate of interest. It simple interest instead of compound were reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years, by Rs 61. Find the sum

A. Rs. 7000

B. Rs. 8000

C. Rs. 7500

D. Rs. 6500

295. In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C?

A. 50

B. 50/9

C. 8500/9

D. 500/9

E. None of these

Explanation :

A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m.

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296. The average age of all the student of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.

A. 15

B. 45

C. 30

D. 50

Explanation :

Let Boys in class = B

Girls in class = 20

Now, (20B+15*20)/(B+20) = 18

⇒ B = 30

297. 0 6 24 60 120 210 ?

A. 343

B. 280

C. 335

D. 295

E. 336

Explanation :

0 6 24 60 120 210 ?

+6 +18 +36 +60 +90 +126

+12 +18 +24 +30 +36

Hence number is 210+114 = 324

298. 32 49 83 151 287 559 ?

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A. 1118

B. 979

C. 1103

D. 1120

E. 1110

Explanation :

32 49 83 151 287 559 ?

+17 +34 +68 +136 +272 +544

+17 +34 +68 +136 +272

So answer is 559 + 544 = 1103.

299. 462 552 650 756 870 992 ?

A. 1040

B. 1122

C. 1132

D. 1050

E. 1124

Explanation :

462 552 650 756 870 992 ?

+90 +98 +106 +114 +122 +130

+8 +8 +8 +8 +8

So next number is 992 + 130 = 1122.

P a g e 166 | 580

300. The average age of a woman and her daughter is 42 years. The ratio of their ages is 2 : 1 respectively. What is the daughter’s age?

A. 28 years

B. 48 years

C. 52 years

D. 31 years

E. 25 years

Explanation :

Let the age of mother be M and that of her daughter be D

Therefore, M+D/2 =42 and M/D=2/1

Solving the above equations we get D = 28 yrs

301. The price of sugar is increased by 25%.Find by how much percent the consumption of sugar be decreased so as not to increase the expenditure?

A. 25%

B. 40%

C. 20%

D. 30%

E. None of these

Explanation :

Using the formula to calculate % decrease as [R/(100+R)]x100 where R = percentage increase in price, we get

Required % decrease in consumption = 25/125 × 100 = 20%

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302. A car travels a distance of 45 km at the speed of 15 km/hr. It covers the next 50 km of its journey at the speed of 25km/hr and the last 25 km of its journey at the speed of 15 km/hr. What is the average speed of the car?

A. 40 km/hr

B. 24 km/hr

C. 15 km/hr

D. 18 km/hr

E. 20km/hr

Explanation :

We know, Average speed = Total distance travelled / Total time taken

Average = 45+50+25/3+2+25/15= 18kmph.

303. A car travels a distance of 170 km in 2 hours partly at a speed of 100 km/h and partly at 50 km/h. The distance travelled at a speed of 50 km/h is

A. 50 km

B. 40 km

C. 30 km

D. 60 km

E. 45 km

Explanation :

Suppose he covers x km at 100 kmph

he covers 170-x at 50 kmph

Solving this equation, we get x = 140.

he covers 30km at 50 kmph.

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304. Even after reducing the marked price of a transistor by Rs. 32, a shopkeeper makes a profit of 15%. If the cost price be Rs. 320, what percentage of profit would he have made if he had sold the transistor at the marked price?

A. 25%

B. 20%

C. 10%

D. 15%

E. None of these

Explanation :

Let x be the marked price,

So x - 32 = 320 × 1.15 ⇒ x = 400.

So required value is

400 = 320 (1 + profit/100),

So profit is 25%

305. The sum of five numbers is 260. The average of first two numbers is 30 and average of the last two numbers is 70. What is third number?

A. 33

B. 60

C. 75

D. Can't determined

E. None of these

Explanation :

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(a + b + c + d + e)/5 = 260 ...........(1)

(a + b)/2 = 30 , Therefore a + b = 60

(d + e)/2 = 70 , Therefore d + e = 140

Using the values in (1) , We get

c= 60

As sum of first two is 60 & sum of last two is 140 so third no. is 260 - 60 - 140 = 60.

306. 20 boys and 32 girls form a group for social work. During their membership drive same no. of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 3:4 respectively?

A. 75

B. 86

C. 68

D. 82

E. 84

Explanation :

Let x be the new boys as well as girls , Therefore

Solving this we get x = 16

So total will be 36 + 48 = 84

307. The simple interest on Rs. 4000 in 3 years at the rate of x% per annum equals the simple interest on Rs. 5000 at the rate of 12% per annum in 2 years. The value of x is

A. 8%

B. 9%

C. 10%

D. 6%

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308. If (4x - 3)/x + (4y - 3)/y + (4z - 3)/z = 0, then the value of 1/x + 1/y + 1/z is

A. 4

B. 6

C. 9

D. 3

Explanation :

(4x - 3)/x + (4y - 3)/y + (4z - 3)/z = 0

=> 4x/x - 3/x + 4y/y - 3/y + 4z/z - 3/z = 0

=> 3/x + 3/y + 3/z = 4 + 4 + 4 = 12

=> 1/x + 1/y + 1/z = 12/3 = 4

309. Find the simplest value of 2√50 + √18 - √72 (given √2 = 1.414)

A. 10.312

B. 8.484

C. 4.242

D. 9.898

Explanation :

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310. A number x when divided by 289 leaves 18 as a remainder. The same number when divided by 17 leaves y as a remainder. The value of y is

A. 3

B. 1

C. 5

D. 2

Explanation :

Here, the first divisor (289) is a multiple of second divisor (17)

∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1. Hence the answer is option 2.

311. An equation of the form ax + by + c = 0 where a ≠ 0, b ≠ 0, c = 0 represents a straight line which passes through

A. (0,0)

B. (3,2)

C. (2,4)

D. None of these

Explanation :

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Ax+by+c = 0

When c = 0

ax+by = 0

by = -ax ⇒ y = - ax/b

when x = 0, y = 0 i.e., this line passes through the origin (0,0).

312. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

A. -4/8

B. 2/7

C. 3/8

D. 3/7

Explanation :

Original fraction = (x - 4)/x

In case II,

8(x - 4 - 2) = x + 1

⇒ 8x - 48 = x + 1

⇒ 7x = 49 ⇒ x = 7

∴Original fraction

= (7 - 4)/7 = 3/7

313. The simple interest on Rs. 4000 in 3 years at the rate of x% per annum equals the simple interest on Rs. 5000 at the rate of 12% per annum in 2 years. The value of x is

A. 8%

B. 9%

C. 10%

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D. 6%

Explanation :

S.I = Principal*Time*Rate/100

Therefore 4000*3**/100 = 5000*2*12/100 => * 5*2*12/4*3

=10% per annum

314. If x2 – 3x + 1 = 0, then the value of x2 + x + 1/x + 1/x2 is

A. 6

B. 8

C. 10

D. 2

Explanation :

x2 - 3x + 1 = 0

=> X2 + 1 - 3x

Dividing both sides by x, => X + 1/3 - 3

Therefore x2 + x + 1/x + 1/x2

= (x2 + 1/x2) + (x + 1/x)

= (x + 1/x)2 -2+ (x + 1/x)

= 9-2 + 3 = 10

315. If (4x - 3)/x + (4y - 3)/y + (4z - 3)/z = 0, then the value of 1/x + 1/y + 1/z is

A. 4

B. 6

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C. 9

D. 3

Explanation :

Z(4x - 3)/x + (4y - 3)/y + (4z - 3)/z = 0

=> 4x/x - 3/x + 4y/y - 3/y + 4z/z - 3/z = 0

=> 3/x + 3/y + 3/z = 4 + 4 + 4 = 12

=> 1/x + 1/y + 1/z = 12/3 = 4

316. Find the simplest value of 2√50 + √18 - √72 (given √2 = 1.414)

A. 10.312

B. 8.484

C. 4.242

D. 9.898

Explanation :

317. A number x when divided by 289 leaves 18 as a remainder. The same number when divided by 17 leaves y as a remainder. The value of y is

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A. 3

B. 1

C. 5

D. 2

Explanation :

Here, the first divisor (289) is a multiple of second divisor (17)

∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1. Hence the answer is option 2.

318. An equation of the form ax + by + c = 0 where a ≠ 0, b ≠ 0, c = 0 represents a straight line which passes through

A. (0, 0)

B. (3, 2)

C. (2, 4)

D. None of these

Explanation :

Ax+by+c = 0

When c = 0

ax+by = 0

by = -ax ⇒ y = - ax/b

when x = 0, y = 0 i.e., this line passes through the origin (0,0).

319. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

P a g e 176 | 580

A. -4/8

B. 2/7

C. 3/8

D. 3/7

Explanation :

Original fraction = (x - 4)/x

In case II,

8(x - 4 - 2) = x + 1

⇒ 8x - 48 = x + 1

⇒ 7x = 49 ⇒ x = 7

∴Original fraction

= (7 - 4)/7 = 3/7

320. In a triangle ABC, ∠A = 90°, ∠C = 55°, AD bar ⊥ BC bar. What is the value of ∠BAD?

A. 45

B. 55

C. 35

D. 60

Explanation :

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321. Eight litres are drawn from a cask full of wine and the cask is filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in case to that of water is 16:65. How much wine did the cask hold originally?

A. 18 litres

B. 24 litres

C. 32 litres

D. 42 litres

E. None of these

Explanation :

Ratio of the quantity of wine now left in case to that of water is 16:65

So out of total 81 units 16 units is wine.

Wine left : total solution = 16:81

As 8 litres are drawn off and replaced by water and is repeated 3 times more

This means (2/3)4

So after one removal ratio of wine and water = 2:3

It means (3u-2u)1 unit = 8 litres

3 unit = 8*3 = 24 litres

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322. A copper wire is bent in the form of an equilateral triangle and has area 121√3cm2 . If the same wire is bent into the form of a circle. The area (in cm2) enclosed by the wire is (take - 22/7)

A. 364.5

B. 693.5

C. 346.5

D. 639.5

E. None of these

323. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively?

A. 166 : 22

B. 83 : 22

C. 83 : 44

D. 78 : 55

Explanation :

E. None of these

Three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively.

Petrol : kerosene

(4:1 = 5)7

(5:2 = 7)5

(6:1 = 7)5

28:7 =35

25:10=35

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30:5 =35

83:22

324. Mrs. Sharma invests 15% of her monthly salary, i.e., Rs. 4428 in Mutual Funds. Later she invests 18% of her monthly salary on Pension Policies also she invests another 9% of her salary on Insurance Policies. What is the total monthly amount invested by Mrs. Sharma?

A. Rs. 113356.8

B. Rs. 12398.4

C. Rs. 56678.4

D. Can't determined

E. None of these

Explanation :

15% of monthly salary = Rs 4428

So monthly salary = Rs 29500

Total money invested = 42% of 29500 = Rs 12398.4

325. If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work ?

A. 20 1/2 days

B. 22 1/2 days

C. 24 1/2 days

D. 25 days

E. None of these

Explanation :

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D = 18 7/8*30/21 = 22 1/2 days

326. lf 3 cannon firing 4 rounds in 6 minutes kill 250 men in half an hour, how many cannon, firing 3 rounds in 5 minutes will kill 600 men in an hour ?

A. 4 cannon

B. 5 cannon

C. 6 cannon

D. 8 cannon

E. 9 cannon

Explanation :

In first case round fired in one min = 4/6 and in second round = 3/5 Therefore new cannons required = 3 5/2*600/250*1/2 = 9

327. Nine students of a class contribute a certain sum. Seven of them give Rs. 5 each. The remaining two give Rs. 5 and Rs. 9 more than the average contribution of all the 9 students respectively. The average contribution of the class of 9 students is -

A. Rs. 10

B. Rs. 14

C. Rs. 7

D. Rs. 12

Explanation :

Let the average contribution of class = x (7 5) + (x + 5) + (x + 9) = 9x 35 + 2x + 14 = 9x 49

= 7x x = 7.

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328. One-fourth of my marks in English is equal to one third of my marks in Hindi, The total number of marks secured by me in both the subjects is 140. The marks secured by me in English are ...

A. 60

B. 80

C. 75

D. None of these

Explanation :

Let marks in English = x & Hindi = y.

x/4 = y/3 Also x + y = 140. Solving the 2 equations we get x = 80.

329. Percent profit earned when an article is sold for Rs. 546/- is double the percent profit earned when the same article is sold for Rs. 483/-. If the marked price of the article is 40% above the cost price, what is the marked price of the article?

A. Rs. 588/-

B. Rs. 608/-

C. Rs. 616/-

D. Rs. 596/-

E. Rs. 586/-

Explanation :

Let profit be P and C.P.= x

Now, x+2P=546

x+P=483

subtracting both,

P=63

P a g e 182 | 580

x=483-63=420

M.P.= 1.4*420=588

330. C is 40% efficient less than A. A and B together can finish a piece of work in 10 days. B and C together can do it in 15 days. In how many days A alone can finish the same piece of work?

A. 18

B. 12

C. 14

D. 20

E. 15

Explanation :

Let work is completed by A in A days

work is completed by B in B days

work is completed by C in C days

Given that, C= A/0.6

Also 1/A+1/B=1/10

1/B+1/C==1/15

Solving Equations A=12

DIRECTIONS for questions 331 to 335: Refer to the graph and answer the given question:

P a g e 183 | 580

331. What is the difference between the total number of scarves sold by store M in 2003 and 2004 together and total number of scarves sold by store N in 2005 and 2006 together?

A. 160

B. 100

C. 140

D. 150

E. 120

Explanation :

Total Number of scarves sold store M in 2003 and 2004= 190+320= 510

Total Number of scarves sold store M in 2005 and 2006=260+370= 630

Difference between the total Number of scarves sold store M in 2003 & 2004 and

Total Number of scarves sold store N in 2005 and 2006 is = 630 – 510 = 120.

P a g e 184 | 580

332. Number of scarves sold by store M decreased by what percent from 2004 to 2005?

A. 40 5/8

B. 45 3/8

C. 42 3/8

D. 30 3/8

E. 35 5/8

Explanation :

Percentage decrease in the number of scarves sold by score M =

320-190/320 * 100 = 130/320 * 100 = 40 5/8%

333. If the respective ratio between total number of scarves sold by stores M and N together in 2002 and that in 2009 is 15 : 11, what is the total number of scarves sold by stores M and N together in 2009?

A. 430

B. 450

C. 420

D. 460

E. 440

Explanation :

Ratio between total number scarves sold by stores M & N together in 2002 and that in 2009 is 15:11.

Total number scarves sold by stores M & N together in 2002 = 240+360 = 600

According to question,= 600/x = 15/11 Or, x = 440

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Total number scarves sold by stores M & N together in 2009 = 440.

334. If the total number of scarves sold by stores M and N together in 2008 is 10% more than that in 2006, what is the total number of scarves sold by stores M and N together in 2008?

A. 638

B. 406

C. 414

D. 396

E. 408

Explanation :

Total number of scarves sold by stores M & N in 2006 = 210+370 = 580

Total number of scarves sold by stores M & N in 2008 = 580×110/100 = 638

335. What is the average number of scarves sold by store N in 2003, 2004 and 2005?

A. 260

B. 270

C. 290

D. 250

E. 290

Explanation :

Average number of scarves sold store N in 2003, 2004 & 2005 = 300+250+260 /3 = 270

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336. What is the central angle corresponding to number of bags available in store T? (In degrees)

A. 91.2

B. 95.6

C. 93.6

D. 94.2

E. 92.5

Explanation :

Central angle corresponding to number of bags available in store T = 26/100*360= 93.6 Deg

337. What is the difference between the average number of bags available in stores P and R together and the average number of bags available in stores S and T together?

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A. 12

B. 22

C. 15

D. 18

E. 20

Explanation :

Average percentage of bags available in stores P and R together = 35%/2 = 17.5%

Average percentage of bags available in stores S and T together = 40%/2 = 20%

Difference between Average Number of bags available in stores P and R together and

Average Number of bags available in stores S and T together = (20% - 17.5%) of 600 = 15

338. The respective ratio between number of bags available in store P in August and that available in the same store in July was 5: 4. How many bags were available in store P in August as compared to July?

A. 150

B. 90

C. 24

D. 60

E. 45

Explanation :

Number of bags available in P store in July = 20% of 600 = 120.

Now, since we have

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Number of bags available in store P in August : Number of bags available in P store in July = 5:4

=> P : 120 = 5 : 4

Thus, number of bags available in Store P (In August) = (5/4)x120 = 150

Universities Total Number of faculty members Percentage of Assistant professors Number of Associate professors

J 250 60 75

K 180 75 24

L 150 80 16

M 100 63 21

339. What is the difference between the total number of Associate Professors in Universities J and M together and the total number of Professors in the same universities together?

A. 54

B. 55

C. 68

D. 58

E. 53

Explanation :

Total number of Associate professor in universities J and M together = 75+21= 96

Total number of professor in universities J and M together = 25+16= 41

Difference between the Total number of Associate professor in universities J and M together and Total number of professor in universities J and M together= 96- 41= 55

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340. In University M, 8/21 of the Assistant Professors are males and in University L, 3/5 of the Assistant Professors are males. What is the respective ratio between male assistant Professors in University M and that in University L?

A. 2:5

B. 1:3

C. 3:5

D. 2:7

Explanation :

341. A Chartered Accountant applies for a job in two firms X & Y. The probability of his being selected in firm X is 0.7, and being rejected at Y is 0.5 and the probability of rejection at least one of his applications is 0.6. What is the probability that he will be selected in one of the firms?

A. 0.8

B. 0.2

C. 0.4

D. 0.7

Explanation :

P(X) = 0.7, P(Y) = 0.5 and P(X &union; Y) = 0.4. Therefore, P(X &intersection; Y) = P(X) + P(Y) – P(X &intersection; Y) = 0.7 + 0.5 – 0.4 = 0.8

342. Two small circular parks of diameters 16 m, 12 m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park has to occupy the same space as the two small parks?

A. 15m

B. 10m

C. 20m

D. 25m

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343. A conical vessel of base radius 2 cm and height 3 cm is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius 2 cm. The kerosene level in the jar is

A. π cm

B. 1.5 cm

C. 1 cm

D. 3 cm

Explanation :

Let the level of kerosene in the cylinder = H.

volume of cone = volume of the cylinder

=> 1/3π(2)2(3) = π(2)2H => H = 1 cm

344. The angle of elevation of an aeroplane from a point on the ground is 45°. After 15 seconds flight, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 m, the speed of the plane in km per hour is

A. 208.34

B. 306.72

C. 402.56

D. 527

Explanation :

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Let the plane at the start is at point C and after 15 seconds it reaches point D after covering x km as shown in diagram.

In Δ ABC, tan 45° = BC/AB => 1 = BC/AB => AB = BC = 3,000.

In %Delta; ADE, tan 30°= ED/(AB+BE) => 3000/(3000+BE) => BE = 2196 m .

Therefore x = 2.196 km.

So aeroplane covers 2.196 km in 15 seconds, so speed of aeroplane = (2.196 x 60 x 60)/15 = 527kmph.

345. At the first stop on his route, a driver unloaded 2/5 of the packages in his van. After he unloaded another three packages at his next stop, 1/2 of the original number of packages remained. How many packages were in the van before the first delivery?

A. 25

B. 10

C. 30

D. 36

Explanation :

Let the packages = P. Therefore, after first delivery he unloaded 2/5 of P and then he unloaded 3

more packages. So total packages unloaded = 2/5 of P + 3. According to the given condition

2/5 of P + 3 = 1/2 of P => P = 30

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346. If S is 150 percent of T, then T is what percent of S + T?

A. 40%

B. 100/3%

C. 75%

D. 80%

Explanation :

S = 1.5 T. Now T/(S + T) x 100 = T/2.5T x 100 = 40%

347. An investor earns 3% return on 1/4th of his capital, 5% on 2/3rd and 11% on the remainder. What is the average rate of return he earns on his total capital?

A. 10%

B. 5%

C. 5.5%

D. 10.5%

Explanation :

Let the capital be C.

Therefore, 3% of 1/4 C + 5% of 2/3 C + 11% of (C - 1/4C - 2/3C) = R % of C => R = 5%

348. Mixture of milk and water has been kept in two separate containers. Ratio of milk to water in one of the containers is 5 : 1 and that in the other container is 7 : 2. In what ratio should the mixtures of these two containers be added together so that the quantity of milk in the new mixture may become 80%?

A. 3 : 2

B. 2 : 3

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C. 4 : 5

D. None of these

Explanation :

Let x litres of mixture be taken from container having 5 : 1 ratio and y litres be taken from 7 : 2 mixture container.

Therefore, according to the given condition,

So they should be mixed in ratio 2 : 3

349. Rahul started a business with a capital of Rs. 8,000. After six months, Sanjay joined him with an investment of some capital. If at the end of the year each of them gets an equal amount as profit, how much did Sanjay invest in the business?

A. Rs. 17,500/-

B. Rs. 18,000/-

C. Rs. 16,000/-

D. Rs. 16,500/-

Explanation :

Rahul’s investment

= Capital × Time period = 8000 × 12. Sanjay’s Investment = C × 6.

As both of them share equal profit, so Rahul’s investment = Sanjay’s investment

=> 8000 × 12 = C × 6 => C = Rs. 16,000.

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350. Sita buys a fridge at 15/16 of its original value & sells it for 10 % more than its value. Then gain % is

A. 15.55

B. 11.67

C. 16.67

D. None of these

Explanation :

Let the original price be O. Cost price = of O and selling price = 1.1 of O.

Gain% = 11/10 of O-15/16 of O / 15/16 of O * 100 = 17.33%

DIRECTIONS for the questions 3 to 4: In the following series, one of the terms given is wrong. Find that term and mark that as your answer.

351. 2 3 10 39 178 885

A. 855

B. 178

C. 10

D. 304

E. 39

Explanation :

The logic is ×1+1, ×2+4, ×3+9, ×4+16, ×5+25,….

So following the logic we get 178 is wrong instead it should be 172. …..

352. 139 150 149 174 223 304

A. 149

B. 150

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C. 174

D. 304

E. 223

353. The figure given below, MNP is an equilateral triangle and LMNO is a square with side 6 cm. What is the area of the pentagon PMLON

A. 72√3 cm2

B. 36√3 cm2

C. 6( 3 + √3 ) cm2

D. 9( 4 + √3 ) cm2

E. 48√3 cm2

354. What is the total cost of construction of a 1m wide path outside the rectangular plot along all the four sides, given the following 2 condtitions :

I. Perimeter of the plot in 260 m and cost of construction of the path is Rs. 850 per m2

II. Area of the plot is 4125 m2 and cost of construction of the path is Rs. 850 per 2

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A. The data in statement II alone are sufficient the question the question, while the data in statement I alone are not sufficient to answer the question.

B. The data in both the statements I & II are insufficient to answer the question.

C. The data either in statement I alone or in II statement alone are sufficient to answer the question.

D. The data in both the statements I & II together are necessary to answer the question.

E. The data in Statement I alone are sufficient to the question, while the data in statement II alone are not sufficient to answer the question.

Explanation :

By using both the statements together ,

The perimeter of plot ,2( L + B ) = 260m Area of plot, L × B = 4125 m2,

Solving these two equations :

we can find that the length of the plot is 75m and the breadth of the plot is 55m.

Now we can easily find the area of the path all around the rectangular plot.

Also the cost of construction is same as Rs 850/m2. Hence we can find the total cost of construction of the path.

356. In the stream running at 3 kmph, a motorboat goes 12 km upstream and returns back to the starting point in 128 minutes. What is the speed of the boat in still water? (in kmph)

A. 20

B. 12

C. 15

D. 25

E. 10

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Explanation :

Let speed of boat in still water = x km/hr

Speed of stream = 3 km/hr

Speed downstream = ( x + 3 ) km/hr,

Speed upstream = ( x - 3 ) km/hr

Therefore according to question,

12/( x - 3 ) + 12/( x + 3 ) = 128/60

Solving ,we get x = 12 km/hr.

357. The respective ratio between ages of P and Q is 11: 7. The respective ratio between P’s age 2 years ago and Q’s age 2 years hence is 7:5. Find the respective ratio between P’s age 7 years hence and Q’s age 7 years ago?

A. 17:9

B. 15:7

C. 19:13

D. 13:5

E. 17:7

Explanation :

Let the present ages of P and Q be 11x,7x respectively. According to the question => (11x - 2)/(7x + 2) = 7/5 => x = 4

Ratio of P’s age 7 years hence & Q’s age 7 years ago = (11 × 4 + 7)/(7 × 4 - 7) = 51/21 = 17/7

358. A jar was containing 60 liters of mixture of milk and water in the ratio 7:5. From this jar 12 litres of mixtures was taken out and 8 litres of pure milk was added. What is the respective ratio of milk and water in the mixture after the final operation?

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A. 9:5

B. 4:3

C. 9:7

D. 6:5

E. 9:3

Explanation :

Let n be the mixture quantity of milk = 7/12 × 60 Ltr. = 35 Ltr.

Quantity of water = 5/12 × 60 Ltr. = 25 Ltr.

12 Ltr. of mixture removed contains milk = 7/12 × 12 Ltr. = 7 Ltr and water = 5/12 × 12 Ltr = 5 Ltr

After adding 8Ltr of pure milk,

Net milk in the mixture = 35 - 7 + 8 = 36 Ltr.

Net water in the mixture = 25 - 5 = 20 Ltr.

So the required ratio of milk and water now = 36/20 = 9:5

359. A project manager estimated that he would complete the project in time if he hires 42 people for 38 days. At the end of 30 days he realized that only 3/5th of the work is complete. How many more men does he need to hire to complete the work in time?

A. 71

B. 47

C. 63

D. 60

E. 75

Explanation :

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42 people in 30 days did 3/5th of the work

Let x people are required to complete the remaining 2/5th of the work in 8 days

Applying chain rule we get x = 42 × 30/8 × (2×5)/(3×5) = 105 people

Additional no. of people required = ( 105 - 42 ) = 63.

360. A basket contains 3 blue, 5 black and 3 red balls. If two balls are drawn at random, what is the probability that none of them is blue?

A. 22/55

B. 3/55

C. 28/55

D. 9/11

E. None of these

Explanation :

Here n(S) = 11C2

Now, two balls can be drawn from 5(black)+3(red) balls = 8 balls in 8C2 ways

∴ n(E) = 8C2

Now, P(E) =

8C2/11C = 28/55

Other method:

Required probability

= 1 - (27/55) = 28/55

361. A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?

A. 2/11

B. 8/11

C. 9/11

D. 3/11

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E. None of these

Explanation :

Selecting 1 black ball out of 5 = 5C1 ways

Selecting on red ball out of 3 = 3C1 ways

The required probability = (5C1 × 3C1)/11C2 = 3/11

362. What should come in place of question mark (?) in the following number/alphabetic series?

24 ? 109 134 150 159

A. 71

B. 65

C. 86

D. 53

E. None of these

363. A boat takes 8 hours to cover a distance while travelling upstream, whereas while travelling downstream it takes 6 hours. If the speed of the current is 4 kmph, what is the speed of the boat in still water?

A. 12 kmph

B. 28 kmph

C. 16 kmph

D. Cannot be determined

E. None of these

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Explanation :

No matter if the boat goes upstream or downstream, Distance covered is same. So we can simply equate the two distances.

We have (x+4) × 6 = (x-4) × 8

Where x = speed of the boat in still water

Now, 6x + 24 = 8x - 32 or x = 28

Hence, the required speed = 28 km/hour

364. A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money.

A. 10%

B. 24%

C. 45%

D. 18%

E. 5%

Explanation :

Let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.

365. A man while returning from his factory, travels 2/3 of the distance by bus, 3/4 of the rest by car and remaining by foot. If he travels 2 km on foot, find the distance covered by him.

A. 24km

B. 22km

C. 28km

D. 26km

E. None of these

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Explanation :

Let total distance be D kms

2/3D + 1/3*3/4D + 2 = D

Therefore D = 24 km

Or going by options

Bus = (2/3) * 24 = 16,

Remaining = 24 - 16 = 8, car = (3/4) * 8 = 6

Total distance = 16 + 6+ 2 = 24km

366. Mira’s expenditure and saving are in the ratio 3:2. Her income increases by 10%. Her expenditure also increases by 12%. By how much % do her saving increase?

A. 7%

B. 9%

C. 10%

D. 13%

E. None of these

Explanation :

Let total income be = 5

Increased income will be = 5.5

Increased expenditure will be = 3.36

Increased saving will be = 5.5 - 3.36 = 2.14

Percentage increase will be = (14/2) * 100 = 7%<

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367. A thief goes away in a car at a speed of 60 kmph. A cop starts chasing the thief after 15 minutes in a car at a speed of 80 kmph. When will the cop overtake the thief from the start?

A. 30 minutes

B. 36 minutes

C. 40 minutes

D. 45 minutes

E. 50 minutes

Explanation :

In 15 minutes thief will be 15 Km away . There will be a gap of 15 Km between thief and police . This gap will be covered with a relative speed of 80 -60=20 Km/h .So thief will be overtaken in 15/20 hours= 45 minutes.

368. A shopkeeper sells sugar at a profit of 20% and uses a weight which is 25 % less. What is total % gain?

A. 45%

B. 22.5%

C. 55%

D. 60%

E. None of these

Explanation :

Let cost of 1 gram of sugar is 1 Rs.

So cost price of 1000 gram is 1000Rs.

As per question, Selling price of 1000 gram is 1200 Rs.

But he uses weight 25% less i.e. 750 gram for a Kg.

So SP of 750 gram is 1200 Rs. while its CP is 750 Rs.

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Hence profit %=450/750 =3/5=60%

369. In an examination it is required to get 296 of the total maximum aggregate marks to pass. A student gets 259 marks and is declared failed. The difference of marks obtained by the student and that required to pass is 5%. What are the maximum aggregate marks a student can get?

A. 690

B. 780

C. 740

D. 749

E. None of these

Explanation :

Let the aggregate marks be x

Therefore, 296 - 259 = 37 will be 5% of the x

Thus, (5/100) * x = 37

=> x = 740

370. Shyama invested Rs. P for 2 years in scheme A which offered 11% p.a. simple interest. She also invested Rs. 600 + P in scheme B which offered 20% compound interest (compounded annually), for 2 years. If the amount received from scheme A was less than that received from scheme B, by Rs. 1216, what is the value of P?

A. Rs. 1,500

B. Rs. 1,400

C. Rs. 2,000

D. Rs. 1,600

E. Rs. 1,800

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Explanation :

Money Invested=P at 11% Simple interest.

P+600 At 20% C.I.

Given that,

1.2P+1216=1.44(P+600)

Or 0.22P= 352

Hence P=1600

371. A vessel contains 180 litres of mixture of milk and water in the respective ratio of 13 : 5. Fifty-four litres of this mixture was taken out and replaced with 6 litres of water, what is the approximate percentage of water in the resultant mixture?

A. 41

B. 31

C. 24

D. 9

E. 17

Explanation :

Milk: water = 13:5

Volume of solution=180 l

Solution taken out= 54 l

Volume of solution left= 180-54=126 l

In 126 l solution,

Milk= 126*13/18= 91 l

Water=126*5/18=35 l

As 6 l water is added

Water= 35+6= 41 l

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Total solution volume= 126+6= 132 l

Percentage of water= 41/132*100= 31 %

372. A started a business with an investment of Rs. 28,000. After 5 months from the start of the business, B and C joined with Rs. 24,000and Rs. 32,000 respectively and withdrew Rs. 8000 from the business. If the difference between A’s share and B’s share in the annual profit is Rs. 2,400, what was the annual profit received?

A. Rs. 15,600

B. Rs. 14,400

C. Rs. 14,040

D. Rs. 15,360

E. Rs. 13,440

Explanation :

Equivalent Contribution of A= 28000*5+20000*7= 280000

Equivalent Contribution of B= 24000*7= 168000

Equivalent Contribution of C= 32000*7= 224000

Let total profit be X.

Given that,

280000X/672000 – 168000X/672000=2400

112000/672000*X=2400

or X=2400*672/112

X=14400

373. The sum of two numbers is equal to 15 and their arithmetic mean is 25 per cent greater than their geometric mean. Find the numbers.

A. 5 & 10

B. 3 & 12

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C. 1 & 14

D. 6 & 9

Explanation :

AM of 2 numbers is a+b/2 GM of 2 numbers is √ab When sum of 2 numbers is 15, their AM is 7.5. AM = 1.25 (GM)

GM = 7.5/1.25 = 6. Hence 36 = ab. So product of 2 numbers is 36. Try by options B is the correct answer.

374. The product of the digits of a two-digit number is twice as large as the sum of its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.

A. 36

B. 27

C. 63

D. None of these

Explanation :

Go by options. 3rd option is the answer because 63 = product of digits = 6 3 = 18. Sum of digits = 6 + 3 = 9.

Hence product of digits is twice as the sum of the digits. Also 63 – 27 = 36. So digits are reversed.

375. Dhruva gave 35% of her monthly salary to her mother. From the remaining salary, she paid 18% towards rent and 42% she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 43,920. What was her monthly salary?

A. Rs. 80,000

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B. Rs. 75,000

C. Rs. 64,000

D. Rs. 76,000

E. Rs. 72,000

Explanation :

Let ‘x’ be the monthly salary, then

(65/100 × 40/100)x + 35/100x = 43920

Solving, X= 72000

376. 18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of 2 : 1. If the resultant respective ratio of milk and water in the vessel was 4 : 1, what was the quantity of pure milk added in the vessel? (in litres)

A. 4

B. 8

C. 10

D. 12

E. 2

Explanation :

80(M) + 18(W) = 98

49 liters sold => 49 is left

40(M) + 9(W)

Let x be the quantity of pure milk added

Given, (40 + 2x)/(9 + x) = 4/1

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Solving, x = 2

377. A pipe can fill a cistern in 12 minutes and another fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two are kept open for 6 minutes in the beginning and then the third pipe is also opened, in what time is the cistern emptied?

A. 54 min

B. 56 min

C. 58 min

D. 60 min

E. 57 min

Explanation :

First two pipe’s one minute work = 1/12 + 1/15 = 5+4/60 = 9/60 First two pipe’s 6 minutes work = 9/60 6 = 9/10. Now one minutes work of three pipes = 1/12 + 1/15 - 1/6 = -1/60 -ve sign shows that if all pipes are opened together they will empty the full cistern in 60 minutes. Now we have 9/10 of cistern filled with water. Time taken to empty 9/10 of water in cistern = 9/10 60 = 54 minutes

378. A and B promise to do a work for Rs. 75. A alone can do it in 20 days and B in 30 days, with the help of C they are able to finish it in 8 days. How will A, B and C respectively distributes the wages?

A. Rs. 20, Rs. 30, Rs. 25

B. Rs. 25, Rs. 20, Rs. 30

C. Rs. 30, Rs. 25, Rs. 20

D. Rs. 30, Rs. 20, Rs. 25

E. None of these

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Explanation :

Everybody will get the wages according to their labor

A’s one day work = 1/20 , A’s 8 days work = 8/20 = 2/5 B’s one day work = 1/30 B’s 8 days work = 8/30 = 4/15 Remaining work = 1- 2/5 - 4/15 = 1/3 C did the 1/3 of work in 8 days wages are divided in the ratio of 2/5:4/15:1/3 = 6:4:5 A’s share = 6/15 75= 30 Rs., B’s share = 4/15 75 = 20 Rs. ,C’s share = 5/15 75 = 25 Rs

379. One ball is drawn at random from a box containing 3 red balls, 2 white balls and 4 blue balls, what is the probability that the ball is a red ball?

A. 1/4

B. 1/3

C. 1/5

D. 2/5

E. 2/3

Explanation :

Total possible outcomes = 9. (i.e. One out of 9 balls) [Favourable outcomes

i.e. One out of 3 Red balls] = 3. Reqd Probability = 3/9 = 1/3

DIRECTIONS for the questions 3 to 4: In the following series, one of the terms given is wrong. Find that term and mark that as your answer

380. 40 20 24 30 60 150

A. 24

B. 60

C. 20

D. 150

E. 30

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Explanation :

The logic is ×0.5 , ×1 , ×1.5, ×2 ,×2.5 …..

So following the logic we get 24 is the wrong number and instead it should be 20. Hence 1st option.

381. 29 33 41 50 77 98 157

A. 33

B. 77

C. 50

D. 98

E. 41

Explanation :

The logic is, +4, +8, +9, 27, +16, +64,….

So following the logic we get that 98 is wrong . So Ans is (D)

382. What is the percent profit earned by selling the article after giving 10% discount? I. Had there been no discount offered, the profit earned would have been 30%. II. Selling price of the article after giving discount is Rs. 3510/-

A. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

B. The data either in statement I alone or in statement II alone are sufficient to answer the question.

C. The data in both the statement I & II together are not sufficient to answer the question.

D. The data in both the statements I & II together are necessary to answer the question.

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E. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.

Explanation :

From Statement I, Let CP = Rs.100 then we get MRP = 130 /- If 10% discount is given then SP = Rs. 117

So, P% = 17%. hence I statement is sufficient to answer the question.

From Statement II we cannot determine the cost price in rupees. Hence we cannot find the profit %.

383. The distance between point A and B is 722 km. At 8 am a car starts from point A (towards point B) at 46 kmph and at 10 am another car starts points B ( towards point A) at 38 kmph. At what time will they meet?

A. 6.30 pm

B. 5.30 pm

C. 4.30 pm

D. 5 pm

E. 6 pm

Explanation :

Distance covered by car A from 8 am to 10 am = (46 × 2) km = 92 km

At 10 am the remaining distance between the two cars = 722 km - 92km = 630 km.

Using, Distance = (Relative speed) × time

630 = (46 + 38) × time taken to cross

630/84 = t

t = 71⁄2hr the two cars will meet at 71⁄2 hr from 10am i.e. 5:30 pm.

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384. A & B started a business together by investing Rs. 36000/- and Rs. 42000/- respectively. Both of them invested for one year whereas after 6 months from the start C joined them by investing a certain amount. If they earned an annual profit of Rs. 39,200/- out of which C’s share is Rs. 7350/-. What is the investment of C?

A. Rs. 24000/-

B. Rs. 36000/-

C. Rs. 27000/-

D. Rs. 33000/-

E. Rs. 30000/-

Explanation :

Let the investment of C = Rs x

Ratio of profits of A & B & C

= 36000 × 12 : 42000 × 12 : x × 6

= 72000 : 84000 : x

=> ( Profit of C / Total Profit ) = ( x / 72000 + 84000 + x ) = 7350/39200

On solving, x = 36000.

385. A rectangular plot, 42m long and 32m wide, has two concrete crossroads (of same width) running in the middle of the plot (one parallel to length and the other parallel to breadth). The rest of the plot is used as a lawn. If the area of the lawn is 1064 sq. m., what is the width of the roads?

A. 3m

B. 4.5m

C. 5m

D. 3.5m

E. 4m

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Explanation :

386. A jar was containing 60 liters of mixture of milk and water in the ratio 7:5. From this jar 12 litres of mixtures was taken out and 8 litres of pure milk was added. What is the respective ratio of milk and water in the mixture after the final operation?

A. 9:5

B. 4:3

C. 9:7

D. 6:5

E. 9:3

Explanation :

Let n be the mixture quantity of milk = 7/12 × 60 Ltr = 35 Ltr

Quantity of water = 5/12 × 60 Ltr. = 25 Ltr

12 Ltr. of mixture removed contains milk = 7/12 × 12 Ltr. = 7 Ltr and water = 5/12 × 12 Ltr = 5 Ltr

After adding 8 Ltr of pure milk,

Net milk in the mixture = 35 - 7 + 8 = 36 Ltr.

Net water in the mixture = 25 - 5 = 20 Ltr.

So the required ratio of milk and water now = 36/20 = 9/5

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DIRECTIONS for the question 4: In the following series, one of the terms given is wrong. Find that term and mark that as your answer.

387. 13 16 24 39 73 98

A. 16

B. 73

C. 39

D. 96

E. 24

Explanation :

The first set of differences are

+3,+8,+15,+24,+35,+48

And again the differences are

+5,+7,+9,+11,+13…….which are in AP

So following the logic we get that 73 is wrong. So Ans is B.

388. Equal sums of money were invested in scheme A and scheme B for two years. Scheme A offers simple interest and scheme B offers compound interest (compounded annually) and the rate of interest (p.c.p.a) for both the schemes are same. The interest accrued from Scheme A after two years is Rs. 2560/- and from scheme B is Rs. 2688/-. Had the rate of interest (p.c.p.a) of scheme A been 6% more, what would have been the interest accrued from Scheme A after two years?

A. Rs. 3972/-

B. Rs. 4124/-

C. Rs. 4266/-

D. Rs. 4096/-

E. Rs. 4154/-

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Explanation :

The SI for 2 years=Rs.2560/-

Since simple interest for each year is same.

SI per annum is Rs.1280

CI for 2 years is Rs.2688/-

Since the rate of interest is same

So CI for 1st year is Rs.1280

CI for 2nd year is (Rs. 1280 + Rs.128)

Hence Rate of interest per annum is = 128/1280×100% = 10%

If the rate of interest is increased by 6% then SI for 2 years = 16%/10%×2560 = Rs. 16×256 = Rs.4096.

389. A & B started a business together by investing Rs. 36000/- and Rs. 42000/- respectively. Both of them invested for one year whereas after 6 months from the start C joined them by investing a certain amount. If they earned an annual profit of Rs. 39,200/- out of which C’s share is Rs. 7350/-. What is the investment of C?

A. Rs. 24000/-

B. Rs. 36000/-

C. Rs. 27000/-

D. Rs. 33000/-

E. Rs. 30000/-

Explanation :

Let the investment of C=Rs x

Ratio of profits of A &B &C

=36000×12 : 42000×12 : x×6

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=72000:84000: x

Solving, x = 36000. B option.

390. What are the marks obtained by Harish in Maths ?

I. Average marks obtained by Harish in Maths and economies are 83.

II. Average marks obtained by Harish in Maths and statistics are 92.

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.

B. The data in both the statements I & II together are necessary to answer the question.

C. The data either in statement I alone or in statement II are sufficient to answer the question.

D. The data in both the statements I & II together are insufficient to answer the question.

E. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Explanation :

We cannot find the marks in maths alone even by using both the statements together as average marks will not tell us exact marks in Maths.

Data is insufficient. Hence D option.

391. By what percent is Rajesh’s salary more/less than Mangesh’s ?

I. Salary of Rajesh is Rs. 12000/-.

II. Salary of Rajesh and Mangesh together is Rs 28000/-

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.

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B. The data in both the statements I & II together are necessary to answer the question.

C. The data either in statement I alone or in statement II are sufficient to answer the question.

D. The data in both the statements I & II together are insufficient to answer the question.

E. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Explanation :

By using both the statements together we can find the salary of Mangesh . Hence we can find the percentage change between the salaries of Rajesh and Mangesh. B option.

392. What is the strength of MBA institute where students study only HR, Marketing and Finance ?

I. Number of students studying HR, Marketing and Financial are in the ratio of 2 : 3: 5 respectively.

II. Number of students studying Marketing is more than those studying HR by 800.

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

B. The data either in statement I alone or in statement II alone are sufficient to answer the question.

C. The data in both the statements I & II together are necessary to answer the question.

D. The data in statement II alone are sufficient to answer the question, while the data in statement I alone not sufficient to answer the question.

E. The data in both the statements I & II together are insufficient to answer the question.

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Explanation :

Using both statements together , Let no. of students of HR, marketing and Finance be 2x,3x,5x and also 3x-2x=800

x=800

So total students =2x+3x+5x=10×800=8000. Hence C.

393. A shopkeeper purchased 96 identical shirts @ Rs. 220/- each. He spent Rs. 3800/- on transport and packing and fixed a marked price of Rs. 450/- each shirt. However, he decided to give discount of 20% on the marked price of each shirt. If he could sell all the shirts, what is the approximate percent profit earned by him?

A. 44

B. 39

C. 33

D. 31

E. 30

Explanation :

Cost of 96 shirts=Rs96×220=Rs.21120

Cost of transportation and packaging =Rs3800

Total Cost price (CP)

=Rs 3800+21120 = Rs24920

Marked Price (MP) of 1 shirt =Rs.450

Discount=20% of Rs450

Net Selling Price (SP) of 1 shirt

=80% of Rs450 = Rs360

Total SP of 96 shirts =Rs 360×96=Rs.34560

Profit Percentage = (SP - CP)/CP * 100%

(34560 - 24920)/24920 * 100% = 38.68% = 39%. Hence, option B.

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394. A school room is to be built to accommodate 70 children, so as to allow 2.2 m2 of floor and 11 m3 of space for each child. If the room be 14 metres long, what must be its breadth and height?

A. 12 & 5.5 metres

B. 13 & 6 metres

C. 11 & 5 metres

D. 11 & 4 metres

Explanation :

22 × 70 = 154 m2 for 70 students.

11 × 70 = 770 m3 for 70 students.

Matching through options answer is 3rd option.

395. Two pipes P and Q can fill a cistern in 3 and 6 minutes respectively, while an empty pipe R can empty the cistern in 4 minutes. All the three pipes are opened together and after 2 minutes pipe R is closed. Find when the tank will be full

A. 3 minutes

B. 6 minutes

C. 5 minutes

D. 8 minutes

Explanation :

1/3 + 1/6 – 1/4 = 3/12.

Work done = 3 × 2 = 6.

Remaining work = 12 – 6 = 6

Hence in addition to 2 minutes, 1 minute more will be needed. So answer is 1st option.

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396. There is a leak in the bottom of a cistern. Before the leak, it could be filled in 4 1/2 hours. It now takes 1/2 hour longer. If the cistern is full, in how much time would the leakage empty the full cistern?

A. 23 hours

B. 35 hours

C. 52 hours

D. 45 hours

Explanation :

2/9 – 1/x = 1/5.

x = 45 hours.

397. Two filling pipes A and B can fill a tank in 30 and 20 hours respectively. Pipe B alone is kept open for half the time and both pipes are kept open for the remaining time. In how many hours, will the tank be completely full?

A. 25 hours

B. 40 hours

C. 15 hours

D. 28 hours

Explanation :

1/30 + 1/20 = 5/60.

Let tank will be completely full in x hours.

x/2 × 1/20 + x/2 × 1/12 = 1.

So x = 15.

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Hence, 3rd option.

398. A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more. Find the distance

A. 60 km

B. 45 km

C. 30 km

D. 20 km

Explanation :

Distance = Speed × Time.

Distance = (Speed+4) (Time-30/60).

Distance= (Speed-2) (Time+20/60).

Solving all equations we get Time = 3 hours,

Speed = 20 km/h.

So, Distance=20 x 3 = 60km

399. The average speed of a train is 20% less on the return journey than on the onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is

A. 60 km/hr

B. 40 km/hr

C. 50 km/hr

D. 55 km/hr

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Explanation :

Let speed of onward journey = x km/h.

Equation will be = 500/x +500/0.8x = 22.5.

By solving we can get the answer as 40 km/h which is 2nd option.

400. Two trains move from station A and station B towards each other at the speed of 50 km/hr and 60 km/hr. At the meeting point, the driver of the second train felt that the train has covered 120 km more. What is the distance between A and B?

A. 1320 km

B. 1100 km

C. 1200 km

D. 960 km

Explanation :

Do this question through options we get the answer as 1st option.

401. Rohit took a loan of ` 20,000 to purchase an LCD TV set from a finance company. He promised to make the payment after three years. The company charges compound interest at the rate of 10% per annum for the same. But, suddenly the company announces the rate of interest as 15% per annum for the last one year of the loan period. What extra amount does Rohit have to pay due to this announcement of the new rate of interest?

A. 1320 km

B. 1100 km

C. 1200 km

D. 960 km

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Explanation :

20000(1+10/100)3,

20000(1+10/100)2(1+15/100) = 27830.

So taking the difference = 1210.

402. A tree was planted three years ago. The rate of its growth is 30% per annum. If at present the height of the tree is 670 cm, what was the height of the tree when it was planted?

A. 305 cm

B. 500 cm

C. 405 cm

D. 625 cm

Explanation :

Let 3 years ago the height of tree = x cm.

After 3 years = x(130/100)3 = 670.

⇒ x=305

403. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs 300 more. The sum is

A. 5300

B. 5500

C. 5000

D. None of these

Explanation :

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Increase of 3% fetched Rs.300 more.

It is for 2 years.

For 1 year Increase of 3% will fetch Rs.150.

So 1 % will fetch Rs.50

100% = 5000.

404. The difference between the simple interest received from two different sources on Rs 3 lakhs for 2 years is rs 1,500. The difference between their rates of interest is

A. 0.20%

B. 0.3%

C. 0.25%

D. 0.4%

Explanation :

Let x and y be the interest rates.

x% of 3 lakhs – y% of 3 lakhs = 1500

(x– y) % of 3 lakhs = 1500

300000(x – y)/100 = 1500

(x – y) = 0.5% for 2 years For 1 year = 0.25%

405. A square tin sheet of side 12 cm is converted into a box with open top in the following steps: The sheet is placed horizontally. Then, equal-sized squares, each of side x cm, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?

A. 1

B. 4

C. 3

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D. 2

Explanation :

Volume of the box = l × b × h = (12 – 2x) (12 – 2x) (x)

Putting x = 1, 2, 3, 4, we get the maximum value of the above equation at

x = 2. So maximum v = 128. i.e. 4th option

406. A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of these is 1.5 cm and 2 cm respectively. The diameter of the third ball is

A. 3 cm

B. 2.66 cm

C. 2.5 cm

D. 5 cm

Explanation :

The sum of the volumes of the new balls will equal the volume of the original ball. So, 1.53 = 0.753 + 13 + r3. Solving this equation gives r = 1.25

So, d = 2.5 cm.

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407. A cylinder is filled to 4/5th of its volume. It is then tilted so that the level of water coincides with one edge of its bottom and top edge of the opposite side. In the process, 30 cc of the water is spilled. What is the volume of the cylinder?

A. 75 cc

B. 100 cc

C. 96 cc

D. Data Insufficient

Explanation :

When tilted, the water level will form the diagonal of the tank and the volume of the water will he half that of the cylinder. Suppose the volume of the cylinder is V. Since 30 ml = 30 cc has spilled out, 4V/5 = 1/2 V + 30.

Solving this equation gives V = 100 cc.

408. A and B invest Rs 3 lakhs and Rs 4 lakhs in a business. A receives Rs 1,000 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year 'A' totally receives X 39,000, what does B receive?

A. 63,000

B. 46,000

C. 36,000

D. 26,000

Explanation :

A and B invest in the ratio 3 : 4.

A receives 1000 per month so he will get 12000 for a year.

If A receives 39000 in total then 39000 – 12000 = 27000 will be his share.

If 3x = 27000, then 4x = 36000.

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409. In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for whole time. Find A's share of the total profit of Rs 2,300.

A. 110

B. 10

C. 100

D. 101

Explanation :

Let the total capital is 6 and time is also 6 years.

A invests 1 for 1 year.

B invests 2 for 2 years

Then, C invests 6 – (1 + 2) = 3 for 6 years.

The ratio of investment is A : B : C = 1 : 4 : 18

If total profit is Rs 2300 then A's share

= 1/23 x 2300 = Rs 100

410. A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another Rs 2,70,000 and C, at the end of 2 years invests Rs 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of A, B and C.

A. Rs 2,70,000; Rs 80,000 and Rs 3,60,000

B. Rs 1,70,000; Rs 1,80,000 and Rs 3,60,000

C. Rs 2,70,000; Rs 1,80,000 and Rs 3,60,000

D. Rs 2,70,000; Rs 1,80,000 and Rs 3,00,000

Explanation :

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1st year, A = 3x, B = 2x and C = 4x

2nd year, A = 3x, B = 2x + 270000 and C = 4x

3rd year, A = 3x, B = 2x + 270000 and

C = 4x + 270000

Total investment by A, B and C is

A = 3x + 3x + 3x = 9x

B = 2x + 2x + 2x + 270000 + 270000

= 6x + 540000

C = 4x + 4x + 4x + 270000 = 12x + 270000

After three years the ratio is 3 : 4 : 5

x = 90000.

Thus initial investment

= (3 * 90000): (2 * 90000): (4 * 90000)

` 270000, ` 180000, ` 360000

411. Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?

A. 10 gallons

B. 12 gallons

C. 14 gallons

D. 13 gallons

Explanation :

The ratio of milk to total volume of the mixture in the 3 vessels is 8/9, 1/6 and 1/2 respectively. We can consider these values as 16/18, 3/18 and 9/18 respectively. By alligation, we get the ratio in which the two mixtures are mixed

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as 6:7 respectively. Since the total quantity is 26, the quantity from the 2nd vessel is (7/13) * 26 = 14 gallons.

412. Meera purchased 23 bracelets at the rate of Rs 160 per bracelet. At what rate per bracelet should she sell the bracelets so that profit earned is 15% ?

A. Rs. 184/-

B. Rs. 186/-

C. Rs. 192/-

D. Rs. 198/-

E. None of these

Explanation :

Since the CP of each bracelet is Rs 160, to make a profit of 15%, the SP should be 160 × 1.15 = Rs 184.

413. Kajal spends 55% of her monthly income on grocery, clothes and education in the ratio of 4 : 2 : 5 respectively. If the amount spent on clothes is Rs. 5,540/-, what is Kajal's monthly income ?

A. Rs. 55,400/-

B. Rs. 54,500/-

C. Rs. 55,450/-

D. Rs. 55,650/-

E. None of these

Explanation :

Let the amount spent on grocery, clothes and education is x. We have 2x/11 = 5540. So, x = Rs. 30470. This is 55% of the total income. Hence total income = (30470 X 100)/55 = Rs 55400.

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414. 35 percent of a number is two times 75 percent of another number. What is the ratio between the first and the second number respectively?

A. 35 : 6

B. 31 : 7

C. 23 : 7

D. 32 : 9

E. None of these

Explanation :

Let two numbers be a and b. Now, 35% of a = 2 times 75% of b. solving we get a : b = 30 : 7 Therefore, the correct answer is option E (none of these).

415. Area of a rectangular field is 3584 m2 and the length and the breadth are in the ratio 7 : 2 respectively. What is the perimeter of the rectangle ?

A. 246m

B. 292m

C. 286m

D. 288m

E. None of these

416. Last year there were 610 boys in a school. The number decreased by 20 percent this year. How many girls are there in the school if the number of girls is 175 percent of the total number of boys in the school this year ?

A. 854

B. 848

C. 798

D. 782

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E. None of these

Explanation :

The number of boys this year = 0.8 × 610 = 488. Since the girls are 175% of the boys, So, the number of girls = 175% of 488 = (175 × 488)/100 = 854

417. Aryan got 350 marks and Vidya scored 76 percent marks in the same test. If Vidya scored 296 marks more than Aryan, what were the maximum marks of the test ?

A. 650

B. 900

C. 850

D. 950

E. None of these

Explanation :

Aryan scored =350, Vidya scored 296 more than Aryan i.e. 350 + 296 = 646. Also, Vidya scored 76% of maximum marks. So, 76% of maximum marks = 646 => maximum marks = 850

418. A student was awarded certain marks in an examination. However, after re-evaluation, his marks were reduced by 40% of the marks that were originally awarded to him so that the new score now became 96. How many marks did the student lose after re-evaluation?

A. 58

B. 68

C. 63

D. 56

E. 64

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Explanation :

Since the student has lost 40% marks, So, he has 60% of the original marks say x. => 0.6 x = 96 => x = 160. Hence, marks lost by him is 160 - 96 = 64.

419. Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number ?

A. 31

B. 29

C. 25

D. 35

E. None of these

Explanation :

Since the average of all five numbers is 61, so the total of all five numbers is 61 × 5 = 305. Total of Ist and IIIrd numbers = 138 and total of IInd and IVth numbers is 138. So the fifth number is 305 - 138 -138 = 29.

420. The respective ratio between the present ages of father, mother and daughter is 7 : 6 : 2. The difference between mother's and the daughter's age is 24 years. What is the father's age at present?

A. 43 years

B. 42 years

C. 39 years

D. 38 years

E. None of these

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Explanation :

The ratio between the present ages of father, mother and daughter is 7 : 6 : 2. Let their ages be 7x, 6x and 2x respectively. Now, we have, 6x - 2x = 24 => x = 6. Hence, age of father is 6 × 7 = 42 years.

421. Average weight of 19 men is 74 kgs. and the average weight of 38 women is 63 kgs. What is the average weight (rounded off to the nearest integer) of all the men and the women together

A. 59kgs

B. 65kgs

C. 69kgs

D. 67kgs

E. 71kgs

Explanation :

The average weight of all men and women = (19x74+38x63)/57 = 66.6 = 67kgs

422. A basket contains 3 blue, 5 black and 3 red balls. If 3 balls are drawn at random what is the probability that all are black?

A. 2/11

B. 1/11

C. 3/11

D. 8/33

E. None of these

Explanation :

Ways of selecting 3 black balls out of 5 - 5C3

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Total ways of selecting 3 balls - 11C3The required probability =

5C3 / 11C3 = 10/165 = 2/33

DIRECTIONS for questions 423-424: What should come in place of question mark (?) in the following number/alphabetic series?

423. 17 9 10 ? 35 90

A. 21

B. 27.5

C. 19

D. 16.5

E. None of these

Explanation :

17×0.5+0.5=9

9×1+1=10

10×1.5+1.5=16.5

16.5×2+2=35

35×2.5+2.5=90

Hence, the question mark(?) should be replaced by 16.5

424. 3 20 78 334 1696 ?

A. 8410

B. 9836

C. 10206

D. 1150

E. None of these

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Explanation :

3×2+14=20

20×3+18=78

78×4+22=334

334×5+26=1696

1696×6+30=10206

Hence, the question mark should be replaced by 10206

425. The magnitude of the area of a circle is seven times that of its circumference. What is the circumference (in units) of the circle?

A. 616

B. 132

C. 88

D. Can't be determined

E. None of these

Explanation :

We have πr2 = 7 x 2πr

∴ r = 14

∴ circumference = 2πr = 2 x (22/7) * 14 = 88

426. 15.002 × ? × 25.0210 = 7113.018

A. 19

B. 26

C. 11

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D. 31

E. 35

Explanation :

15.002 × ? × 25.0210 = 7113.018

427. A mixture of 45 liters of spirit and water contains 20% of water in it. How much water must be added to make the water 25% in the new mixture?

A. 5 liters

B. 3 liters

C. 4 liters

D. 6 liters

E. None of these

Explanation :

Quantity of water in the mixture = (20/100) x 45 = 9 L

Let x litres of water must be added to make the water 25 % in the solution

Therefore, [(9+x)/(45+x)] x 100 = 25

⇒ 36 + 4x = 45 + x

⇒ 3x = 9

⇒ x = 3 litres

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428. The sum of four consecutive integers is 102. Find the product of the extremes:

A. 548

B. 684

C. 648

D. 578

E. None of these

Explanation :

a,a+1,a+2,a+3 , let these be the numbers.

Sum=102⇒4a+6=102⇒4a=96⇒a=24

Hence extremes=24 , 27

24X27=648

429. A bottle contains 3/4 of milk and the rest water. How much of the mixture must be taken away and replaced by equal quantity of water so that the mixture has half milk and half water?

A. 25%

B. 331⁄2%

C. 45%

D. 50%

E. None of these

Explanation :

Let the total quantity of mixture = 1 liter.

Now supposing x liters of mixture is withdrawn which contains 3/4x milk and rest water.

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So, according to the question 3/4 -3/4x =1/2.

Solving x = 1/3 which means 1/3 of mixture is to be withdrawn to serve the purpose.

430. Krishan has some hens and some cows. If the total number of animal heads are 59 and the total number of feet are 190, how many cows does Krishan have?

A. 36

B. 32

C. 23

D. 20

E. Can't be determined

Explanation :

Suppose he has x cows and y hens.

So x + y = 59 and 4x + 2y = 190.

Solving these two equations, we get x = 36.

So option A is the answer

431. The height of a room is 5 metres and its length is twice its breadth. If 240 metres of paper of breadth 50 cm are required for papering its walls, find the area of the floor.

A. 128 m2

B. 64 m2

C. 320 m2

D. 32 m2

E. None of these

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Explanation :

H = 5, L = 2B, Area of 4 = Area of wall paper

2(LH) + 2(BH) = 240 × 50/100

10L + 10 B = 24 × 5, 10L + 5L= 24 × 5

15 L = 24 × 5, L =24×5/15 = 8

L= 8, B = 4,

∴area of floor = L × B

= 8 × 4 = 32

432. The respective ratio of salaries of A and B is 8:7, if the salary of B increases by 20% and the salary of A increases by 21% the new ratio becomes 96 : 77 respectively. What is A's salary?

A. Rs. 22,560/-

B. Rs. 21,600/-

C. Rs. 20,640/-

D. Rs. 23.040/-

E. Cannot be determined

Explanation :

Only ratio of the salary is given, but salary is not given, so we cannot determined the salary of A . Hence answer is option E.

433. (1/3)rd the diagonal of a square is 2. What is the measure of the side of the concerned square?

A. 12 m

B. 9 m

C. 18 m

D. 6 m

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E. 7 m

Explanation :

Let a be the side of a square.

Therefore, diagonal (d) = √2a

We are given that

Hence the answer is option B.

434. (√4356 * √?) / √6084 = 11

A. 144

B. 196

C. 169

D. 81

E. 121

435. M, N, O and P divided Rs. 44,352/- among themselves M took (3/8)th of the money, N took (1/6)th of the remaining amount and the rest was divided among O and P in the ratio of 3:4 respectively. How much did O get as his share?

A. Rs. 9,600/-

B. Rs. 20,600/-

C. Rs. 10,300/-

D. Rs. 8,700/-

E. Rs. 9,900/-

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Explanation :

Share of M = (3/8) * 44352 = 16632/-

Remaining amount = 44352 – 16632 = 27720/-

Share of N = (1/6) * 27720 = 4620/-

Remaining amount = 27720 – 4620 = 23100/-

Share of O = (3/7) * 23100 = 9900/-

436. 3 ? 14 55 274 1643

A. 11

B. 5

C. 6

D. 8

E. 7

Explanation :

>Here the given pattern is:

3 ? 14 55 274 1643

The pattern:

3 × 2 – 1 = 5, 5 × 3 – 1 = 14

14 × 4 – 1 = 55, 55 × 5 – 1 = 274

274 × 6 – 1 = 1643, So ? = 5

437. The perimeter of a rectangle whose length is 6m more than its breadth is 84m. What would be the area of a triangle whose base is equal to the diagonal of the rectangle and whose height is equal to the length of the rectangle? (in m2)

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A. 324

B. 372

C. 360

D. 364

E. 348

Explanation :

Let l, b and d be the length, breadth and diagonal of the rectangle

Therefore, l – b = 6 and 2(l + b) = 84 or l + b = 42

Solving the above equations, we get l = 24m and b = 18m

Therefore, d2 = ( l2 + b2) Putting the values, we get

d2 = 242 + 182 = 576 + 324 = 900 => d = 30m

Let b and h be the base and height of the triangle

We are given that b = d = 30m and h = l = 24m

Thus, area of triangle = (1/2)bh = (1/2) * 30 * 24 = 360 m2

438. The sum of the series (1 + 0.6 + 0.06 + 0.006 + 0.0006 + ....) is

A. 1 2/3

B. 1 1/3

C. 2 1/3

D. 2 2/3

Explanation :

1 + 0.6 + 0.06 + 0.006 + 0.0006 + … = 1.666 ….. = 1.6 = 1 6/9 = 1 2/3

439. A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be

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A. 1

B. 2

C. 7

D. 17

Explanation :

If the first divisor is a multiple of second divisor, then the remainder in second case = remainder obtained by dividing the first remainder by the second divisor.

Remainder = 21 ÷ 19 = 2

440. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is

A. 45 : 56

B. 45 : 51

C. 47 : 56

D. 47 : 51

Explanation :

Let the CP be Rs. 100

SP = Rs 112

If the marked price be Rs. x, then 90% of x = 112

=> x = 112*100/90 = Rs. 1120/9

= 900 : 1120 = 45 : 56

441. By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

A. Rs. 2,600

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B. Rs. 2,700

C. Rs. 2,800

D. Rs. 3,000

Explanation :

CP of bicycle

= 100/114 * 2850 = Rs. 2500

SP for a profit of 8%

= 108/100 * 2500 = Rs. 2700

442. If A's income is 50% less than that of B's, then B's income is what per cent more than that of A?

A. 125

B. 100

C. 75

D. 50

Explanation :

Required percentage

= 50/100-50*100 = 100%

443. Simple interest on a certain sum is 16/25 of the sum. The rate percent if the rate per cent and time (in years) are equal, is

A. 6%

B. 8%

C. 10%

D. 12%

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Explanation :

Interest/Principal = 16/25

Therefore Rate = S.I * 100/Principal*Time

=> x = 16/25*100/x

⇒ x2 16 × 4 = 64

⇒ x = √64 = 8% per annum

444. If the difference between S.I. and C.I. for 2 years on a sum of money lent at 5% is Rs. 6, then the sum is

A. Rs. 2200

B. Rs. 2400

C. Rs. 2600

D. Rs. 2000

Explanation :

Difference = Pr2/10000

=> 6 = P*5*5/10000

=> P = 6 * 400 = Rs. 2400

445. At what percentage above the cost price must an article be marked so as 10 gain 33% after allowing customer a discount of 5% ?

A. 48%

B. 43%

C. 40%

D. 38%

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Explanation :

Condition

Let it be marked up by x%

A.T.C. (Successive % age females)

x-5-5x/100=33,

x = 40

446. Two persons start walking at a steady pace of 3 km/hour from a road intersection along two roads that make an angle of 60° with each other. What will be the shortest distance separating them at the end of 20 minutes?

A. 3kms

B. 2kms

C. 1.5kms

D. 1kms

447. X and Y work on a job together for four days and complete 60% of it. X takes leave and then Y works for 8 more days to complete the job. How long X will take to complete the entire job alone ?

A. 6 days

B. 8 days

C. 10 days

D. 11 days

448. A number when divided by 5 leaves remainder 3. What is the remainder when the square of the same number is divided by 5?

A. 1

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B. 3

C. 0

D. 4

Explanation :

Remainder is a part of the number. So , whatever happens with the number, happens with the remainder also. Square of remainder is 9.which will be divded by 5 leaving remainder 4.

449. If 40% of the number exceeds the 25% of it by 54. Find the number

A. 360

B. 420

C. 560

D. 600

Explanation :

0.4x - 0.25x = 54. x = 360.

450. Among three numbers, the first is twice the second and thrice the third. If the average of three numbers is 49.50, then what is the difference between the first and the third number?

A. 28

B. 54

C. 39.50

D. 41.50

6x, 3x, 2x.

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Explanation :

Now average = 6x+3x+2x/9 = 39.5

On solving we get the difference in between first and the third number = 54.

451. Rita can knit a pair of socks in 3 days. Sita can knit the same in 6 days. If they are knitting together, in how many days will they knit two pairs of socks.

A. 4

B. 1

C. 2

D. None of these

Explanation :

1 /3+ 1/6 = 1 /2 Together they will take, 1/ 1/2 = 2

452. The HCF and LCM of two numbers are 21 and 4641 respectively. If one of number lies between 200 and 300, the two numbers are

A. 273, 357

B. 273, 361

C. 273, 359

D. 273, 363

Explanation :

Note that 273 is common in all the options

HCF × LCM Product of 2 numbers

21 × 4641 =273x, x = 357

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453. The fare on a commodity is diminished by 10% and its consumption increases by 10%. The collection of the revenue derived from it is K% change. The value of K is

A. 0

B. -1

C. 1

D. 2

454. In a Express Train passengers traveling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio 1:2:3, and fare to each class in the ratio 5:4:2. If the income from this train is Rs. 57000, the income of A.C. Sleeper Class is

A. Rs. 8000

B. Rs. 12000

C. Rs. 15000

D. Rs. 6000

Explanation :

Income is divided in the ratio 1×5:2×4:3×2= 5:8:6.

Now 5x + 8x + 6x = 19x = 57000.

∴ x =3000.

Therefore income from A.C. Sleeper Class = 3000 . 5=15000.

455. A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy?

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A. 100 m, 15

B. 100 m, 16

C. 120 m, 15

D. 120 m, 16

Explanation :

Since it is given that length is sufficient for 6mt. and 8 mtr. gaps so it must be a common multiple of 6 & 8 which out of choices can be 120 meters only. Now as a concept to generate 15 gaps (= 120/8), you need 16 poles. So, answer is 4th option.

456. The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is

A. 1960

B. 3240

C. 1540

D. None of these

Explanation :

Required no. of ways = No. of ways of selecting 3 ladies & 4 gentlemen - No. of ways of selecting them when X & Y got selected

= 8C3 × 7C4 - 7C2 × 6C3 = 1960 - 420 = 1540.

Thus, option C is correct.

457. Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together, they can complete the job in 4 days, then the time taken by each of them separately to complete the work is

A. 36, 24 and 16 day

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B. 20, 16 and 12 days

C. 24, 12 and 8 days

D. None of these

Explanation :

We are given that R = 2M = 3S. This means that Suresh is thrice efficient than Ramesh and Mahesh is twice efficient than Ramesh.

So let us assume that Ramesh can do 1 unit work per day. so Mahesh will do 2 units per day and Suresh will do 3 units of the work per day.

So the total work done by all three in one day is 6 units. Now they together take 4 days to complete the work.

So the total work is 6 x 4 = 24 units and individually Ramesh, Mahesh and Suresh will take 24 days, 12 days and 8 days respectively.

458. Three sides of a triangular field are 20 meters, 21 meters and 29 meters long, respectively. The area of the field is

A. 215 sq m

B. 230 sq m

C. 210 sq m

D. None of these

Explanation :

The given sides are 20,21,and 29 and 202+212=292

Since it is a right angled triangle, so area = 1/2 * 20 * 21 = 210 sq m.

459. Find the greatest number that will divide 964, 1238 and 1400 leaving remainders 41, 31 and 51, respectively.

A. 71

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B. 81

C. 61

D. 73

Explanation :

We have 964 – 41 = 923, 1238 – 31 = 1207 and 1400 – 51 = 1349.

So the required number is the HCF of 923, 1207 and 1349 which is 71. Hence 1st option.

460. In a rhombus ABCD the diagonals AC and BD intersect at the point (3, 4). If the point 'A' is (1, 2), the diagonal BD has the equation

A. x – y – l = 0

B. x – y + l = 0

C. x + y – l = 0

D. x + y – 7 = 0

Explanation :

Slope of AC = (2-4)/(1-3) = 1. As diagonals in a rhombus bisect each other at 90°, so slope of BD = -1.

Also diagonal BD has to lie on the point (3, 4), so equation of the line is y - 4 = - 1(x - 3) ⇒ x + y – 7 = 0.

461. A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the centre is on the same side of the chords, then the diameter of the circle is of length:

A. 5 cm

B. 6 cm

C. 10 cm

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D. 12 cm

Explanation :

In the given figure, EB = 3 cm, FD = 4 cm, EF = 1 cm

Let OF = a cm

In triangle OFD, r2 =a2+42 in triangle OEB, r2 =(a+1)2+32

Solving the above two equations, we get a = 3cm

Putting the value of a in any of the above equation, we get r = 5 cm

Therefore, diameter = 10 cm.

462. An express train travelled at an average speed of 100 kmph, stopping for 3 minutes after every 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time it took the express train to travel 600 km?

A. 900 km

B. 307.5 km

C. 1200 km

D. 100 km

Explanation :

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For 600 kms. The Express train needs 6 hrs. for the distance travelled @ 100 kmph. and it will stop for ( 600/75)=8.

So there must be 7 stoppages in between where it stops for 3 min. each totalling upto 21 min. So total time will be 6 hrs.21 min.

Now the Local train travelling @ 50 kmph. will cover 300 kms. in 6 hrs. and in rest 9 min. it will travel 7.5 kms.( 300/25=12 stoppages where it will stop for 12 min. So, 21- 12 = 9 ).

The total distance becomes 300 + 7.5 = 307.5 km.

ALTERNATE SOLUTION We can also think that since speed of express train is double the local speed, so local train will tavel less than 600 km, Only option b has such option and hence is the required answer

463. Two alloys contain zinc and copper in the ratio of 2 : 1 and 4 : 1. In what ratio the two alloys should be added together to get as new alloy having zinc and copper in the ratio of 3 : 1?

A. 7:5

B. 5:7

C. 3:5

D. None of the above

Explanation :

Required ratio = (4/5 – 3/4) : (3/4 - 2/3) = 3 : 5

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464. Swati and Rajani enter into a partnership with their capitals in the ratio 5 : 6. At the end of 8 months, Swati withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Rajani's capital was used?

A. 10 months

B. 12 months

C. 14 months

D. None of the above

Explanation :

Let the capital was invested for x months.

So (5 × 8)/(6 × x) = 5/9. Solving this, we get x = 12

465. The odds against a certain event are 5 : 2 and the odds in favour of another independent event are 6 : 5. The probability that at least one of the events will happen is:

A. 12/77

B. 25/77

C. 52/77

D. 65/77

E. None of these

Explanation :

Required probability = 1 – P (NO event will happen) = 1 – (5/7 × 5/11) = 52/77.

466. Number of times the hands of a clock are in a straight line (make 180°) every day is

A. 44

B. 24

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C. 42

D. 22

Explanation :

In 12 hour, the hands of clock make 180° 11 times, thus total of 22 times in 24 hours.

467. A motor boat can travel at 10 km/h in still water. It traveled 91 km downstream in river and then returned, taking altogether 20 hours. Find the rate of flow of river.

A. 3

B. 5

C. 6

D. 7

E. None of these

Explanation :

Let the rate of flow be y kmph. The equation that will be formed is 91/(10+Y) + 91/(10-Y)=20

Solving we get y = 3.

468. If x^4 +(1/{x^4})=47 find the value of x^3 +(1/{x^3}) is

A. 18

B. 20

C. 22

D. 24

E. None of these

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469. A person invests Rs. 5508 in '4% stock at 102'. He afterwards sells out at 105 and reinvests in '5% stock at 126'. What is the change in his income?

A. 20

B. 7

C. 10

D. 9

E. None of these

Explanation :

Old income = 5508/102 × 4 = Rs. 216. No. of shares purchased = 5508/102 = 54. So sale proceeds = (54 × 105) = Rs. 5670.

Therefore, New income = (5670 × 5)/126 = Rs. 225.

So change in income = 225 – 216 = Rs. 9.

470. The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between the measure of their interior angles is 2 : 3. The number of sides of these polygons are respectively

A. 4,8

B. 5,10

C. 6,12

D. 8, 16

E. None of these

Explanation :

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Going by options, if the no of sides are 4 and 8, then the interior angles of the polygons is 90deg and 135deg (int angles = 180°(N-2)/N)

Which are in the ratio 2 : 3. So the answer is 1st option.

471. How many two-digit odd numbers can be formed from the digits 1, 2, 3, 4, 5, if repetition of digit is allowed?

A. 5

B. 15

C. 35

D. 25

E. None of these

Explanation :

Here unit place can be filled in 3 ways (i.e. 1, 3, 5)

Ten's place can be filled in 5 ways. Required number of numbers = 5 x 3 = 15

472. Three equal glasses are filled with mixtures of sprit and water. The ratio of the sprit to water is as follows: in the first glass as 3 : 4, in the second glass as 4 : 5 and in the third glass as 5 : 6.The contents of the three glasses are emptied into a single vessel. What is the ratio of the sprit to water in the mixture now?

A. 920:1159

B. 820:1149

C. 1120:1134

D. 1010 : 1122

E. None of these

Explanation :

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Required Ratio

{(3/7)+(4/9)+(5/11)}/{(4/7)+(5/9)+(6/11)} =920/1159

473. Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?

A. 96

B. 102

C. 106

D. 112

E. None of The above

Explanation :

If both filling pipes are working together, time taken to fill the tank will be 14 X16/(14 + 16) = 112/15 hrs.

But due to leak it takes 32 min more. Hence total time taken = 112/15 + 32/60 = 8 hrs.

Let the leak takes x hours to empty the tank, so, 1/14 + 1/16 - 1/x = 1/8.

By solving we get the answer as 112 hours. So answer is 4th option.

474. In a race of 600 metres, A can beat B by 60 metres and in a race of 500 metres, B can beat C by 50 metres. By how many metres will A beat C in a race of 400 metres?

A. 76 metres

B. 80 metres

C. 70 metres

D. 84 metres

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Explanation :

A runs B runs C runs

600 metres race 600m 540 m

500 metres race 500 m 450m

Combing ratio A runs B runs C runs

300metres - 2700meters - 2430metres

Unitary A runs B runs C runs

Method 400mtres - 360 metres - 324 metres

∴ A beats C by 400-324 = 76 metres.

475. If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 25 men in 3 days?

A. 65mtr.

B. 52mtr.

C. 70mtr.

D. 78mtr.

Explanation :

20 men is 6 days can build 112 metres

25 men in 3 days can build = 112*(25/20)x(3/6)

= 70 meters

476. If the compound interest on a certain sum of money for 3 years at 10% per annum be Rs. 993, what would be the simple interest?

A. Rs. 880

B. Rs. 890

C. Rs. 895

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D. Rs. 900

Explanation :

Let P = Principal

A - Amount

We have a = P(1 + R/100)3 and CI = A - P

ATQ 993 = P(1 + R/100)3 - P

∴ P = Rs 3000/-

Now SI @ 10% on Rs 3000/- for 3 yrs = (3000 x 10 x 3)/100

= Rs 900/-

477. What annual installment will discharge a debt of Rs. 4600 due in 4 years at 10% simple interest?

A. 1000

B. 1030

C. 1100

D. None of these

Explanation :

Let the annual instalment be Rs. 100. The first instalment will be paid one year from now i.e. 3 years before it is actually due. The second instalment will be paid two years from now i.e. 2 years before it is actually due.

The third instalment will be paid 1 year before it is actually due.

The fourth instalment will be paid on the day the amount is actually due.

On the first instalment the interest will be paid for 3 years, on the second for 2 years, on the third for 1 year, on the fourth for 0 year. In total an interest for 6 years will be paid (3 + 2 + 1 + 0) on Rs. 100 @ 10%. Interest = (100 × 6 × 10)/100 = Rs. 60 and the principal is Rs 100 × 4 = Rs 400. The total loan that

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can be discharged is Rs. 400 + 60 = Rs. 460. Here the technique of Chain Rule will be applied. I.e. for Rs. 460 the instalment required is Rs. 100, for Rs. 4600 the instalment required is 4600 × 100/460 = Rs. 1000.

478. A number whose fifth part increased by 5 is equal to its fourth part diminished by 5, is

A. 160

B. 180

C. 200

D. 220

Explanation :

x/5 + 5 = x/4 - 5

⇒ x/5 - x/4 = 10

x/20 = 10

⇒ x = 200

479. Two numbers are such that the ratio between them is 3 : 5, but if each is increased by 10, the ratio between them becomes 5:7. The numbers are

A. 3, 5

B. 7, 9

C. 13, 22

D. 15, 25

Explanation :

No's are in the ratio 3:5

Le the No's be 3x and 5x

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ATQ. (3x+10) : (5x+10) = 5:7

∴ x = 5

No's are (15,25)

480. A man rows downstream 30 km and upstream 18 km, taking 5 hours each time. What is the velocity of the stream (current)?

A. 1.2 km/hr

B. 1.5 km/hr

C. 2.5 km/hr

D. 1.8 km/hr

Explanation :

LET X =SPEED OF BOAT AND Y = SPEED OF CURRENT.

⇒ 30/(X+Y)=18/(X-Y)=5 BY SOLVING Y = 1.2

481. A train 125 metre long is running at 50 km/hr. In what time will it pass a man running at 5 km/hr in the same direction in which the train is going?

A. 25 sec

B. 10 sec

C. 20 sec

D. 15 sec

Explanation :

Distance = 125 metres Speed = 50-5 = 45kmph => 45 * (5/18) = 12.5 m/s

Time = 125 / 12.5 = 10 sec.

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482. A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 42 minutes, will be covered by A in

A. 11 min

B. 14 min

C. 7 min

D. 17 min

Explanation :

B is thrice as fast as C

C covers in 42min

∴ B covers in 42/3 = 14 min

A is twice as fast as B

∴ A covers in 14 * (1/2) = 7 min

483. A worker is kept on a contract for 100 days to make some toys. On any of these 100 days he does not make more than 20 toys. If on any day, he makes more than 12 toys, then he makes at most 6 toys each on the next two days. What is the maximum possible number of toys that he can make over the period of 100 days?

A. 1109

B. 1208

C. 1100

D. 1076

E. None of these

Explanation :

If the worker makes more than 12 toys on any day then in three days period he can make a maximum of 20 + 6 + 6 = 32 toys.

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On the other hand he could have made 36 toys over this span by making 12 toys each day.

So to achieve the maximum he must not make more than 12 toys on any day except possibly the last day.

So, maximum number of toys he could have made = 99 × 12 + 20 = 1208

484. From a list of four comics, four friends discuss their favourite comics. At least 2 friends vote for Mandrake, not more than 3 vote for Mammaji, 1 votes for Alibaba and 2 vote for Tom & Jerry. If two friends have exactly voted for 2 different comics each, and 2 friends for exactly 3 different comics each, then how many votes did Mandrake get?

A. 2

B. 3

C. 4

D. Can’t say

E. None of these

Explanation :

There are a total of 10 votes, of which exactly 3 go to Alibaba and Tom & Jerry together.,

The remaining 7 are distributed between Mandrake and Mammaj

Maximum votes that Mandrake can get is 4 (since there are only 4 comics) and maximum votes that Mammaji can get are 3.

485. From a bag containing 242 balls, one ball weighs 19.9 grams and all the other weigh 19.5 grams each. Using a simple balance where balls can be kept on either pan, what is the minimum weighs required to identify the defective ball?

A. 3

B. 4

C. 5

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D. 7

E. none of the above

Explanation :

By dividing the total balls in three parts and putting two parts on the simple balance we can find which of the three parts has ball of different weight. Again divide this part into further three parts and put two parts on the simple balance. From here again we can find the part having ball with different weight. Again this part can be divided into three parts and so on. So 35 = 243 i.e up to 243 balls can be checked within 5 weighings.

DIRECTIONS for the question 4-5: Read the information given below and answer the question that follows.

Five friends, viz. Shan, Monu, Jai, Karan and Bunty are living in five different cities named Karanpur, Jaipur, Vizanagar, Barnala and Patiala, not necessarily in that order.

Their salaries are 7 Lacs, 8 Lacs, 9 Lacs, 11 Lacs, 13 Lacs (INR per annum), in no particular order. Further, the following information is given about them:

I. Karan, who does not live in Barnala, earns a salary that is a prime number multiple of 1 Lac.

II. Monu made a call to one of his four mentioned friends who lives in Patiala and who earns a perfect square multiple of 1 Lac in salary.

III. Jai's salary is 1 Lac more than the average salary of Karan and Shan

IV. Monu lives in the city, which has the shortest name amongst the above cities.

486. If Karan lives in Vizanagar, then what is the average salary of the persons living in Barnala and Karanpur?

A. 9

B. 10

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C. 12

D. Data insufficient

E. None of these

Explanation :

From the given information, we can summarize the data in the following table:

Karan Jai Shan Bunty Monu

Salaries:7 or 13 11 13 or 7 9 8

Cities: K/V B/K/V B/K/V Patiala Jaipur

Where ‘K’, ‘V’ and ‘B’ stands for ‘Karanpur’, ‘Vizanagar’ and ‘Barnala’ respectively.

If Karan, lives in Vizanagar, then Jai and Shan must be staying at Karanpur and Barnala, not necessarily in that order. Their average salary in any case will be Rs. 12 lakhs or 9 lakhs. So, the data is insufficient.

487. Who stays in Patiala?

A. Shan

B. Monu

C. Bunty

D. Jai

Explanation :

Monu called a friend, who gets Rs. 9 lakh as his salary is a perfect square multiple of 100000 and stays in Patiala.

Bunty stays in Patiala.

488. If Monu and Jai live in cities with names starting with consecutive alphabets, then who lives in Vizanagar?

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A. Shan

B. Monu

C. Bunty

D. Karan

Explanation :

Monu lives in Jaipur, so Jai must be living at Karanpur.

Since Karan is not staying at Barnala, he must be staying at Vizanagar.

489. A square and a regular hexagon have the same area. Find the ratio of the perimeter of the square to the perimeter of the hexagon.

A. √3 : 2

B. 1 : 2

C. 4√3 : 4√4

D. 4√4 : 4√3

490. AnswIf x + y = 1, then what is the value of (x^3 + y^3 + 3xy)?

A. 1

B. 2

C. 9

D. 0

E. None of these

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491. Last Sunday, every customer who visited the CENTRA MALL was given a gift coupon, on every purchase worth Rs. 1000, with a unique six-digit code written on it. Each code was such that-

(i). The first digit was non-zero.

(ii). All the six digits were distinct.

(iii). The 1st and the 6th digits added up to 9 and so do the 2 nd and 5 th digits, and also the 3rd and 4th digits.

A gift was given to a customer who had two coupons with codes such that the numbers formed using the first three digits of each code were the reverse of each other.

The number of coupons distributed could not have been more than

A. 504

B. 729

C. 432

D. 648

E. None of The above

The six-digit number on the coupon will look like

x y z 9 – z 9 – y 9 – x

Once we select the first, second and third digits of the number, the remaining three digits get fixed. The first digit can be chosen out of 1, 2, 3, …9 in 9 ways.

Then, the second digit can be selected in (10 – 2) = 8 ways and the third digit in (10 – 4) = 6 ways.

Hence, the maximum possible number of such six digit number is 9 × 8 × 6 = 432.

492. A basket contains 3 blue, 5 black and 3 red balls. If two balls are drawn at random, what is the probability that none of them is blue?

A. 22/55

B. 3/55

C. 28/55

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D. 9/11

E. None of these

Explanation :

Here n(S) = 11C2

Now two balls can be drawn from 5(black)+3(red) balls = 8 balls in 8C2 ways.

Therefore n(E) = 8C2

Now, P(E) = (8C2/11C2) = (28/55)

Other method:

Required probability

= 1-(27/55) = (28/55)

493. A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?

A. 2/11

B. 8/11

C. 9/11

D. 3/11

E. None of these

Explanation :

Selecting 1 black ball out of 5 - 5C1 ways Selecting on red ball out of 3 - 3C1 ways

he required probability = (5C1 * 3C1) / (11C2) = (5*3) / 55 = 3/11

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494. Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together, they can complete the job in 4 days, then the time taken by each of them separately to complete the work is

A. 36, 24 and 16 days

B. 20, 16 and 12 days

C. 24, 12 and 8 days

D. 20, 18 and 15 days

E. None of these

Explanation :

We are given that R = 2M = 3S. This means that Suresh is thrice efficient than Ramesh and Mahesh is twice efficient than Ramesh. So let us assume that Ramesh can do 1 unit work per day. so Mahesh will do 2 units per day and Suresh will do 3 units of the work per day. So the total work done by all three in one day is 6 units. Now they together take 4 days to complete the work. So the total work is 6 x 4 = 24 units and individually Ramesh, Mahesh and Suresh will take 24 days, 12 days and 8 days respectively.

495. A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money

A. 10%

B. 24%

C. 45%

D. 18%

E. 5%

Explanation :

let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.

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496. What will be the compound interest on a sum of Rs. 7200/- at 5 p.c.p.a. in 2 years?

A. Rs. 841/-

B. Rs. 738/-

C. Rs. 793/-

D. Rs. 812/-

E. Rs.694/-

497. In a rhombus ABCD the diagonals AC and BD intersect at the point (3, 4). If the point 'A' is (1, 2), the diagonal BD has the equation

A. x – y – 1 = 0

B. x – y + 1 = 0

C. x + y – 1 = 0

D. x + y – 7 = 0

E. x + y – 2 = 0

Explanation :

Slope of AC = (2-4)/(1-3) = 1. As diagonals in a rhombus bisect each other at 90°, so slope of BD = -1. Also diagonal BD has to lie on the point (3, 4), so equation of the line is y - 4 = - 1(x - 3) => x + y – 7 = 0.

498. A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the centre is on the same side of the chords, then the diameter of the circle is of length:

A. 5cm

B. 6cm

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C. 10cm

D. 12cm

E. None of these

Explanation :

499. An express train travelled at an average speed of 100 kmph, stopping for 3 minutes after every 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time it took the express train to travel 600 km?

A. 900km

B. 307.5km

C. 1200km

D. 100km

E. 300km

Explanation :

For 600 kms. The Express train needs 6 hrs. for the distance travelled @ 100 kmph. and it will stop for ( 600/75 )= 8. So there must be 7 stoppages in

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between where it stops for 3 min. each totalling upto 21 min. So total time will be 6 hrs.21 min.

Now the Local train travelling @ 50 kmph. will cover 300 kms. in 6 hrs. and in rest 9 min. it will travel 7.5 kms.( 300/25=12 stoppages where it will stop for 12 min. So, 21- 12 = 9 ). The total distance becomes 300 + 7.5 = 307.5 km.

ALTERNATE SOLUTION

We can also think that since speed of express train is double the local speed, so local train will tavel less than 600 km, Only option b has such option and hence is the required answer.

500. In how many different ways can the letters of the word 'PARTY' be arranged?

A. 120

B. 2005

C. 2400

D. 720

E. None of these

Explanation :

Total no. of ways =5 x 4 x3 x 2 x 1 = 120

501. A & B together can complete a piece of work in 16 days, B alone can complete the same work in 24 days. In how many days can A alone complete the same work ?

A. 34 days

B. 50 days

C. 48 days

D. 42 days

E. None of these

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Explanation :

Let A alone can complete the work in x days and B alone can complete the work in 24days.

Therefore, according to the given conditions,

1/x + 1/24 = 1/16,

1/x = 1/48

So, A's one day work is 1/48 which means that A will complete the entire work in 48days.

Therefore, the answer is option C.

502. A and B are partners in a business. They invest in the ratio 5:6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B's investment was used?

A. 12 months

B. 10 months

C. 15 months

D. 14 months

E. 18 months

Explanation :

Ratio of profit is always distributed in the ratio of their investment and time.

5unit × 8 months:6 units × B’s months = 5:9

So B’s investment time = 12 months

503. There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly. Find probability that 1 is red and the other is white.

A. 5/22

B. 5/23

C. 7/22

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D. 4/9

E. None of These

Explanation :

There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly.

probability that 1 is red and the other is white = 3/12× 5/11 = 5/44

504. According to a new plan rolled out by H1SP Bank, the rate of simple interest on a sum of money is 8% p.a. for the first two years, 10% p.a. for the next three years and 6% p.a. for the period beyond the first five years. Simple interest accrued on a sum for a period of eight years is Rs. 12,800. Find the sum.

A. Rs. 24,000

B. Rs. 16,000

C. Rs. 15,000

D. Rs. 13,500

E. None of These

Explanation :

Let the sum of money be x.

So interest in first two years = 8×2 = 16% of x

Interest in next three years = 10×3 =30% of x

Interest in next five years = 6×3 = 18% of x

Total interest = 64% of x = Rs 12,800

We get x = Rs 20,000

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505. Three Science classes A, B and C take a Life Science test. The average score of students of class A is 83. The average score of students class B is 76. The average score of class C is 85. The average score of class A and 8 is 79 and average score of class B and C is 81. Then the average score. Of classes A, B and C is

A. 80

B. 80.5

C. 81

D. None of these

Explanation :

506. A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?

A. 221

B. 343

C. 81

D. 243

E. None of these

507. Solve : (638 + 9709 - 216) ÷ 26 = ?

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A. 275

B. 365

C. 420

D. 300

E. 390

Explanation :

(638 + 9709 - 216) ÷ 26 = 10131/26 = 389.65

Approx 290

508. A dishonest dealer professes to sell his goods at the cost price but uses a weight of 800gm instead of 1kg. Find his real gain percent.

A. 25%

B. 20%

C. 30%

D. None of these

Explanation :

200/800 ×100 = 25%

509. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1,020 after a further period of 5 years. The sum and the rate % are

A. Rs. 500, 5%

B. Rs. 400, 15%

C. Rs. 600, 10%

D. Rs. 700, 20%

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Explanation :

Amount after 2 years = Rs 720

Amount after 7 years = Rs 1020

Therefore, Interest for 5 years = Rs 300

Interest for 1 year = Rs 60

And Interest for 2 years = Rs 120

SO Principal = 720-120 = Rs 600

Also, 120 = (600*R*2)/100 = R = 10%

Amount after 2 years = Rs 720

Amount after 7 years = Rs 1020

Therefore, Interest for 5 years = Rs 300

Interest for 1 year = Rs 60

And Interest for 2 years = Rs 120

SO Principal = 720-120 = Rs 600

Also, 120 = (600*R*2)/100 = R = 10%

510. A train with 90 km/h crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/h. What is the time taken by the second train to cross the bridge ?

A. 61 seconds

B. 63 seconds

C. 62 seconds

D. 64 seconds

Explanation :

Train A, Speed = 90kmph

=90*(5/18)m/s = 25m/s = 25m/s, t=36s

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Let length, L = x+y = time*speed = 25*36 = 900m

=800m, Speed= 45*(5/18) = (25/2) m/s

t= (Distance/Speed) = (800/(25/2)) = (1600/25) = 64 seconds

511. Ramesh travels 760 km to his home, partly by train and partly by car He takes 8 hours, if he travels 160 km by train and the rest by car. He takes 12 minutes more, if he travels 240 km by train and the rest by car. What are the speeds of the train and of the car?

A. Speed of car = 90 km/h, speed of train = 60 km/h

B. Speed of car = 100 km/h, speed of train = 80 km/h

C. Speed of car = 80 km/h, speed of train = 70 km/h

D. Speed of car = 100 km/h, speed of train = 90 km/h

Explanation :

Let speeds be x and y for train and car respectively.

Then 8 = (160/8) + (600/y) .....(1)

And 8(1/5) = (240/x) + ((760-240)/y) .....(2)

Solving for x and y, we get 100 and 80 km/hr.

You can also use the option straightway for such Qs.

512. Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?

A. 15

B. 25

C. 20

D. 30

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Explanation :

By direction options,500/25=20 ,500/20=25

By mathematical method, the main steps are: xy = 500 …(1) and (x−5) (y+5) = 500 …(2),

From eqn. 2, x−y = 5 or y = x−5 Put in eqn 1, x(x−5) = 500 or x2-5x-500=0 ,

i.e. x = 25 and attended ones = x − 5 = 20

513. After being set up, a company manufactured 6000 scooters in the third year and 7000 scooters in the seventh year. Assuming that the production increases uniformly by a fixed number every year, what is the production in the tenth year?

A. 7850

B. 7650

C. 7750

D. 7950

Explanation :

You can use A.P.,Tn =a+(n-1)d ,6000=a+2d.....(1) and 7000 = a + 6d .....(2)

Eqn (2) – Eqn (1) ⇒ 1000=4d,

i.e. d = 250 and a = 6000 − 500 = 5500

T10 =5500 + 9 × 250 =7750

514. The average score of boys in an examination in a school is 71 and that of the girls is 73. The average score of the school is 71.8. The ratio of the number of boys to that of the girls that appeared in the examination is

A. 1 : 2

B. 3 : 2

C. 2 : 2

D. 4 : 2

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Explanation :

71.8 = (71x+73y)/(x+y)

71.8 (x+ y) = 71x + 73y

0.8x = 1.2y

x:y = 12:8 which is equals to 3:2

515. The mean monthly salary paid to 75 workers in a factory is Rs. 5,680. The mean salary of 25 of them is Rs. 5,400 and that of 30 others is Rs. 5,700. The mean salary of the remaining workers is

A. Rs. 5,000

B. Rs. 7,000

C. Rs. 6,000

D. Rs. 8,000

Explanation :

5680*75 = (5400*25+5700*30+x(75-25-30))/75

4,26,00 = 1,35,000 +1, 71,000 + 20x

X = 1,20,000/20, = 6,000

516. A sum of Rs. 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days. How much did C receive if all the four work together?

A. Rs. 14/3

B. Rs. 16/3

C. Rs. 15/3

D. Rs. 17/3

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Explanation :

B+ C's 1 day's work = ½ and B's 1 day's work = 1/20

Therefore, C's 1 day's work = (1/12) – (1/20) = 4/120 = 1/30

Monet will be distributed according to the ratio of work done i.e A: B: C: D

= 1/32 : 1/20 : 1/30 : 1/24 = 15 :24:16:20

Therefore, C's Share = 16/(15+24+16+20) = Rs 16/3

517. A man sold two steel chairs for Rs. 500 each. On one, he gains 20% and on other, he loses 12%. How much does he gain or lose in the whole transaction?

A. 1.5% gain

B. 2% gain

C. 1.5% loss

D. 2% loss

Explanation :

CP/SP = 100/(100±x) , i.e. Total CP = 417 (500*100/200) + 568(500*100/88)≅ 985

Since CP<SP .Therefore, Profit = 100-985 = 15

P% ≅ 15/985 X 100 ≅ 1.5 %

DIRECTIONS for the questions 1 to 10: Solve the following question and mark the best possible option

518. There are two motor cycles (A and B) of equal cost price. Motorcycle A was sold at a profit of 14% and motorcycle B was sold for Rs. 4,290/- more than its cost price. The net profit earned after selling both the motor cycles (A and B) is 20%. What is the cost price of each motorcycle?

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A. Rs. 16,500/-

B. Rs. 16,000/-

C. Rs. 15,500/-

D. Rs. 71,500/-

E. Rs. 17,000/-

Explanation :

Let the cost price of each motorcycle be Rs. ‘A’. So SP of A = 1.14A and SP of B = A + 4290. Total CP = 2A. As net profit is given to be 20% on both the motorcycles, so we can form the equation as (2.14A + 4290 - 2A)/2A = 20%. Solving it further, we get (0.14A + 4290)5 = 2A. Solving this equation, we get value of A as 16,500. Hence answer is option D.

519. A bag contains 3 white balls and 2 black balls. Another bag contains 2 white and 4 black balls. A bag and a ball are picked at random. What is the probability that the ball drawn is white?

A. 7/11

B. 7/30

C. 5/11

D. 7/15

E. None of these

Explanation :

(3/5+2/6)×½, Solving, 7/15

520. A is thrice as efficient as B and takes 10 days less to do a piece of work than B takes to do the same work. In how many days, B alone can finish the whole work?

A. 15 days

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B. 10 days

C. 9 days

D. 8 days

E. 7 days

Explanation :

Efficiency A:B = 3:1

Therefore, no. of days A:B = 1:3

Given, 3x – x = 10

Solving, A = 5 days and B= 15 days.

521. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is ________

A. Rs. 400

B. Rs. 500

C. Rs. 600

D. Rs. 800

E. None of these

Explanation :

Let ‘P’ be the principle

P(1.1)2 – P = 525

P = 2500

S.I = (2500*4*5)/100 = 500

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522. There is a natural number which becomes equal to the square of a natural number when 100 is added to it, and to the square of another natural number when 168 is added to it. Find the number.

A. 189

B. 69

C. 156

D. 224

E. 255

Explanation :

Try by options. 3rd option is correct because 100 + 156 = 256 (square of 16) and 168 + 156 = 324 (square of 18).

No other option is satisfying the 2nd condition.

523. In a rectangular auditorium, chairs are arranged in rows and columns. The number of chairs in each column is more than the number of chairs in each row by 5. If there are in all 300 chairs, find the number of chairs in each row and in each column.

A. 25, 20

B. 30, 10

C. 23, 18

D. 20,15

E. None of these

Explanation :

Go by options. When there were 300 chairs, so product of chairs in rows and chairs in columns should be 300. Difference of 5 should be there between the seats in rows and columns. So no option out of 1st 3 is satisfying the conditions. So answer is 4th option and correct values are 20 and 15.

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524. A started a business with an investment of Rs. 16,000. After 6 months from the start of the business, B and C joined with Rs. 12,000 and Rs. 18,000 respectively and A invested an additional amount of Rs. 4000. If the difference between A’s share and B’s share in the annual profit is Rs. 6000, what was the annual profit received?

A. Rs. 17,600

B. Rs. 13,200

C. Rs. 14,300

D. Rs. 16,500

E. Rs. 11,000

Explanation :

Amount invested by A= 16000 for first 6 months, and 20000 for next 6 months

Amount invested by B= 12000 for 6 months

Amount invested by C= 18000 for 6 months

Now by compound partnership, IA:IB:IC = PA : PB : PC

16000*6 + 20000*6 : 12000*6 : 18000*6 = 6:2:3

Given 6x – 2x= 4x = 6000; x=1500

so total profit = 11x = 16500.

525. Shiva gives 20% of her monthly salary to his mother, 50% of the remaining salary he invests in an insurance scheme and PPF in the respective ratio of 5 : 3 and the remaining he keeps in his bank account. If the sum of the amount he gives to his mother and that he invests in PPF is Rs. 12,600, how much is Shiva’s monthly salary?

A. Rs. 36,000

B. Rs. 64,000

C. Rs. 42,000

D. Rs. 40,000

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E. None of these

Explanation :

Let the total amount be x.

0.2x = given to mother

0.25x= invested in insurance

0.15x= invested in ppf

0.4x= Bank account

Given, 0.2x+0.15x = 0.35x = 12600; x=36000

526. The respective ratio of radii of two right circular cylinders (A and B) is 4 : 7. The respective ratio of the heights of cylinders A and B is 2 : 1. What is the respective ratio of volumes of cylinders A and B?

A. 25 :42

B. 23 : 42

C. 32 : 49

D. 30 : 49

E. 36 : 49

527. C is 20% more efficient than A. A and B together can finish a piece of work in 16 days. B and C together can do it in 15 days. In how many days A alone can finish the same piece of work?

A. 42

B. 48

C. 54

D. 36

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E. 45

Explanation :

Let total of 240 units of work to be done.

Now as given A+ B can do 240/16= 15 units/day

Also B + C can do 240/15= 16 units/day

And given, C= 1.2 A., Substituting and solving the equations we get, A= 5 units/day, ie.e A will complete work in 240/5= 48 days.

528. The odds against a certain event are 5 : 2 and the odds in favour of another independent event are 6 : 5. The probability that at least one of the events will happen is:

A. 12/77

B. 25/77

C. 52/77

D. 65/77

Explanation :

Required probability = 1 – P (NO event will happen) = 1 – (5/7 × 5/11) = 52/77.

529. Number of times the hands of a clock are in a straight line every day is:

A. 44

B. 24

C. 42

D. 22

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Explanation :

In 12 hour, the hands of clock coincide 11 times and they make 180° also 11 times, thus total of 22 times. So in 24 hours, the hands of clock will be forming a straight line 22 + 22 = 44 times.

530. A motor boat can travel at 10 km/h in still water. It traveled 91 km downstream in river and then returned, taking altogether 20 hours. Find the rate of flow of river.

A. 3 kmph

B. 5 kmph

C. 6 kmph

D. 7 kmph

Explanation :

Let the rate of flow be y kmph. The equation that will be formed is 91/(10+y) + 91/(10-y) = 20

Solving we get y = 3.

531. A person invests Rs. 5508 in '4% stock at 102'. He afterwards sells out at 105 and reinvests in '5% stock at 126'. What is the change in his income?

A. Rs. 20

B. Rs. 7

C. Rs. 10

D. Rs. 9

Explanation :

Old income = 5508/102 × 4 = Rs. 216. No. of shares purchased = 5508/102 = 54. So sale proceeds = (54 × 105) = Rs. 5670.

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Therefore, New income = (5670 × 5)/126 = Rs. 225.

So change in income = 225 – 216 = Rs. 9.

532. The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between the measure of their interior angles is 2 : 3. The number of sides of these polygons are respectively:

A. 4, 8

B. 5, 10

C. 6, 12

D. 8, 16

Explanation :

Going by options, if the no of sides are 4 and 8, then the interior angles of the polygons is 90° and 135° (int angles = 180°(N-2)/N)

Which are in the ratio 2 : 3. So the answer is 1st option.

533. How many two-digit odd numbers can be formed from the digits 1, 2, 3, 4, 5, if repetition of digit is allowed?

A. 5

B. 15

C. 35

D. 25

Explanation :

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Here unit place can be filled in 3 ways (i.e. 1, 3, 5)

Ten's place can be filled in 5 ways. Required number of numbers = 5×3 = 15

534. Three equal glasses are filled with mixtures of sprit and water. The ratio of the sprit to water is as follows: in the first glass as 3 : 4, in the second glass as 4 : 5 and in the third glass as 5 : 6.The contents of the three glasses are emptied into a single vessel. What is the ratio of the sprit to water in the mixture now?

A. 920 : 1159

B. 820 : 1149

C. 1120 : 1134

D. 1010 : 1122

Explanation :

Required Ratio:

3/7 + 4/9 + 5/11 / 4/7 + 5/9 + 6/11 = 920 / 1159.

535. Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?

A. 96 hours

B. 102 hours

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C. 106 hours

D. 112 hours

Explanation :

If both filling pipes are working together, time taken to fill the tank will be 14 X16/(14 + 16) = 112/15 hrs. But due to leak it takes 32 min more. Hence total time taken = 112/15 + 32/60 = 8 hrs. Let the leak takes x hours to empty the tank, so, 1/14 + 1/16 - 1/x = 1/8.

By solving we get the answer as 112 hours. So answer is 4th option.

536. If √1+x/961=32/31, then the value of x is

A. 63

B. 61

C. 65

D. 64

537. a and b are odd numbers, then which of the following is even?

A. a + b + ab

B. a + b-1

C. a + b + 1

D. a + b + 2ab

Explanation :

⇒ The sum of two odd number is even. The same is the case with their product.

∴ a + b + 2ab = Even number

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538. The single discount equal to three consecutive discounts of 10%, 12% and 5% is

A. 26.27%

B. 24.76%

C. 9%

D. 11%

Explanation :

Single equivalent discount for 10% and 12%.

⇒ (12 -10 -12*10 /100)% = 20.8%

Single equivalent discount for 20.8% and 5%.

⇒(20.8 -5 -20.8*5/100)% = 20.8%

= 24.76%

539. An alloy contains copper, zinc and nickel in the ratio of 5 : 3 : 2. The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is

A. 8

B. 10

C. 12

D. 15

Explanation :

Let x kg of nickel be mixed.

20+x/100+x= 3/11

⇒ 220 + 11x = 300 + 3x

⇒ 11x - 3x = 300-220

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⇒ 8x = 80 ⇒ x = 10 kg.

540. The ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages five years hence will be 2 : 3. Then the ratio of their present ages is

A. 1:2

B. 3:5

C. 3:4

D. 2:5

Explanation :

Let the ages of Ram and Rahim 10 years ago be x and 3x years respectively.

After 5 years from now,

x+15/3x+15=2/3

⇒ 6x + 30 = 3x + 45

⇒ 3x = 45-30 = 15

⇒ x = 5

∴ Radio of their present ages

= (x+ 10) : (3x + 10)

= 15 : 25 = 3 : 5

541. The ratio between two numbers is 2 : 3. If each number is increased by 4, the ratio between them becomes 5 : 7. The difference between the numbers is

A. 8

B. 6

C. 4

D. 2

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Explanation :

Let the numbers be 2x and 3x.

∴ (2x+4)/(3x+4) = 5/7

⇒ x = 28 – 20 = 8 = Required difference

542. Monthly incomes of A and B are in the ratio of 4 : 3 and their expenses bear the ratio 3:2. Each of them saves Rs. 6,000 at the end of the month, then the monthly income of A is

A. Rs. 12,000

B. Rs. 24,000

C. Rs. 30,000

D. Rs. 60,000

Explanation :

Let the monthly incomes of A and B be Rs. 4x and Rs. 3x respectively and their expenditures be Rs. 3y and Rs. 2y respectively.

∴ 4x – 3y = 6000 and 3x – 2y = 6000

⇒ 4x – 3y = 3x – 2y ⇒ x = y ∴ 4x – 3y = 6000

⇒ x = 6000

⇒ A’s monthly income = 4x = Rs. 24000

543. The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers?

A. 15

B. 17

C. 19

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Explanation :

If the smallest number be x, then

X/3+12=x+2=x+36=3x+6

⇒ 3x – x = 36 – 6 ⇒ 2x = 30 ⇒ x = 15

∴ Third number = 15 + 4 = 19

544. What will be the compound interest on Rs. 18,600/- for 2 years, the rate of interest for first year being 8% and for the second year being 15%?

A. Rs. 4489.90

B. Rs. 4967.20

C. Rs. 4232.80

D. Rs. 4501.20

E. Rs. 3637.10

Explanation :

= 18600(1+8/100)(1+15/100)

⇒18600 (1.08) (1.15) = 23101.2

⇒CI = A – P = 23101.2 – 18600 = 4501.2

Hence, Option 4.

545. The sum of five numbers is 260. The average of the first two numbers is 30 and the average of the last two numbers is 70. What is the third numbers?

A. 33

B. 75

C. 60

D. Cannot be determined

E. None of these

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Explanation :

a+b+c+d+e=260

⇒a+b /2 =30

⇒ a+b=60

⇒ d+e /2 =70

⇒ d + e =140

⇒ 60+c+140=260

⇒ c = 60

Hence , Option 3.

546. A certain number of capsules were purchased for Rs.176/-. 6 more capsules could have been purchased in the same amount if each capsule was cheaper by Rs. 3/-.What was the number of capsules purchased?

A. 13

B. 16

C. 17

D. 8

E. 11

Explanation :

Let ‘n’ be the number of capsules purchased and ‘c’ be the cost of each capsule. cn = 176

(n+ 6) (c – 3) = 176

Now check option

When n = 16, c = 11

Hence, Option 2.

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547. Ram was asked to find 7/8th of a fraction but made the error dividing the fraction by 7/8. As a result of this, he was off the correct answer by 75/784. What answer was Ram supposed to arrive at?

A. 13/32

B. 9/144

C. 5/16

D. 5/14

E. 9/16

Explanation :

ATQ (8/7)y - (7/8)y = 75/784 where y is the req. fraction.

y= 5/14.

Ram is supposed to arrive at (7/8)y = (7/8)*(5/14) = 5/16.

Hence, Option 3.

548. 36 workers can finish a piece of work in 14 days. If the work is to be completed in 8 days, how many extra workers are required

A. 29

B. 33

C. 23

D. 31

E. 27

Explanation :

Let ‘x’ be the extra workers required

work workers Days

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w 36 14

w 36+x 8

⇒ 36*14 = (36 + x).8

⇒ on solving x = 27

Hence, Option 5.

549. A man can row 13 kmph downstream and 9 kmph upstream. What is the speed of the man in still water? (in kmph)

A. 12

B. 10.5

C. 11

D. 10

E. 11.5

Explanation :

Speed of stream = s

Speed of man in still water = b

ATQ

b + s = 13

b – s = 9

⇒ b = 11, s = 2

Hence, Option 3.

550. A is 60% more efficient than B. In how many days will ‘A’ and ‘B’ working together complete a piece of work which ‘A’ alone takes 15 days to finish?

A. 124/13

B. 118/3

C. 56/3

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D. 131/3

E. 120/13

Explanation :

As A is 60% more efficient than B

⇒ We can suppose that if B does 5 units/days then A does 8 units/day.

Work done by A in 15 days = 120 units.

A and B working together do 13 units in a day.

⇒ A and B can do 120 units of work in

120/13 Days.

Hence, Option 5

551. The sum of the digits of a two-digit number is 12 and when the digits of the two-digit number are interchanged, the new number is 36 more than the original number. What is the original two digit number?

A. Cannot be determined

B. 93

C. 48

D. 39

E. 84

Explanation :

Let ‘ab’ be the Required Number

a+b=12….(i)

ATQ ba=ab+36

10b+a=10a+b+36

9(b-a)=36

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b-a=4….(ii)

From eqn. (i) and (ii)

b=8, a=4

⇒ Required Number = 48, Hence, Option (3).

552. A car covers the first 39 kms of its Journey in 40 minutes & covers the remaining 25 kms in 35 minutes. What is the average speed of the car?

A. 40 km/hr

B. 164 km/hr

C. 49 km/hr

D. 48 km/hr

E. None of these

Explanation :

Average Speed = Total Distance Traveled / Total Time Taken

= (64*60)/75 = 51.2 km/hr.

Hence,Option 5.

553. A, B and C entered into a partnership by investing Rs. 64,000/-, Rs. 52,000/- and Rs. 36,000/- respectively. All of them invested for equal period of time. If A got Rs. 35,584/- as his share of annual profit, what amount did C get as his share of annual profit?

A. Rs. 20,632/-

B. Rs. 18,296/-

C. Rs. 21,084/-

D. Rs. 19,768/-

E. Rs. 20,016/-

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Explanation :

As time is same therefore

Profit of C= (36000/64000)*35584 =Rs.20,016/-.

Hence, Option 5.

554. The number missing in the series 2, 5, 10, 17, ?, 37, 50, 65 is?

A. 27

B. 22

C. 25

D. 26

Explanation :

The logic is that consecutive odd numbers starting from 3 are being added to each number.

2, 2 + 3, 5 + 5, 10 + 7, 17 + 9 ( = 26 ), 26 + 11, ...and so on.

555. Which one of the following when divided by 19 gives the quotient 19 and the remainder 9?

A. 370

B. 331

C. 281

D. 368

Explanation :

370 = 19 × 19 + 9.

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556. Ten men finish a piece of work in 10 days. How many men needed to finish the work in 1 day?

A. 10

B. 25

C. 50

D. 100

Explanation :

10 Men can do it in 10 days

=> 100 Men can do it in 1 days.

557. Square root of 625 is

A. 12

B. 15

C. 25

D. 35

Explanation :

√625 = 25.

558. A watch hand reads 4:30. If the minute hand points East, in what direction will the hour hand point?

A. North

B. North-West

C. North-East

D. South-East

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Explanation :

It is North East.

559. Anuj gets 3 marks for each correctly done question but loses 2 marks for each wrongly done question. He attempts 30 questions and gets 40 marks. The number of correctly attempted questions is?

A. 20

B. 25

C. 15

D. 21

Explanation :

For every wrong answer Anuj loses 5 Marks

(90 – x) × 5 = 40 => x = 10

10 wrong and 20 correct.

560. The price of the sugar having risen by 60%, by how much per cent must a householder reduce his consumption of sugar so as not to increase his expenditure?

A. 60%

B. 40%

C. 20%

D. 75/2%

Explanation :

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561. If Tuesday falls on the fourth of the month, what day will dawn three days after the 24th?

A. Tuesday

B. Friday

C. Thursday

D. Monday

Explanation :

04th, 11th, 18th, 25th – Tuesday

=> 24th is Monday.

562. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

A. 145 degree

B. 150 degree

C. 155 degree

D. 160 degree

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563. Hour hand moves 30 degree in 1 hr

=> In 51⁄6How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

A. 5600

B. 6400

C. 7000

D. 7200 it moves = 31/6 * 30 = 155 degree.

Explanation :

Required No. = (800 * 600 * 2.5)/(25 * 11.25 * 6) = 6400.

564. A number is such that when it is multiplied by ‘8’, it gives another number which is as much more than 153 as the original number itself is less than 153. What is 25% of the original number?

A. 8

B. 7.5

C. 10

D. 8.5

E. 6.5

Explanation :

Let the no. be x

Given 8x-153=153-x

Hence x=34

25% of x=8.5

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565. A and B can complete a piece of work in 80 days and 120 days respectively. They started working together but A left after 20 days. After another 12 days C joined B and they completed the work in 28 more days. In how many days can C alone complete the work?

A. 110 days

B. 112 days

C. 114 days

D. 120 days

E. None of these

Explanation :

So efficiency of A and B are 3 units and 2 units respectively.

As they worked for 20 days together after that A left so total unit contribution in 20 days= (3+2) units * 20 days = 100 units

Remaining units = 240 – 100 = 140 units

After another 12 days C joined B and they completed the work in 28

more days, so total units contribution of B in 40 days = 2*40 = 80 units

Remaining units i:e = 140-80 = 60 units

Now 60 units is done by C in 28 days

So to do 240 units C require = 28/60 *240 = 112 days

566. The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is

A. 0

B. 1

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C. 2

D. 3

E. 4

Explanation :

Let the numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

=> xy = 77

∴ Possible pairs = (1,77) and (7,11)

567. What is the least number which, when divided by 5, 6, 7, 8 gives the remainder 3 but is divisible by 9?

A. 1463

B. 1573

C. 1683

D. 1793

E. None of these

Explanation :

LCM of 5, 6, 7, 8 = 35 × 24 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9.

For k = 2, it is divisible by 9.

∴ Required number = 840k + 3

= 840 × 2 + 3 = 1683

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568. By walking at of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is:

A. 75 minutes

B. 60 minutes

C. 40 minutes

D. 30 minutes

E. 20 minutes

Explanation :

4/3 of usual time = Usual time + 20 minutes

1/3 of usual time

= 20 minutes

Usual time = 20 × 3 = 60 minutes

569.

A. 1

B. 0.1

C. 0.01

D. 10

E. 0.001

Explanation :

4.41 x 0.16 / 2.1 x 1.6 x 0.21 =441 x 16 / 21 x 16 x 21 =1

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570. By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:

A. Rs. 2,600

B. Rs. 2,700

C. Rs. 2,800

D. Rs. 3,000

E. Rs.3,500

Explanation :

CP of bicycle = 100/114 x 2850 =Rs 2500

SP for a profit of 8% = 108/100 x 2500 = 2700

571. By selling an article, a man makes a profit of 25% of its selling price. His profit per cent is:

A. 20

B. 25

C. 16

D. 15

E. 33 1/3

Explanation :

If the SP of article be Rs. x then its CP is x - x/4 =Rs. 3x/4

∴ Gain % = (x/4) / (3x/4) x 100 = 100/3 = 33 1/3 %

572. Monthly incomes of A and B are in the ratio of 4 : 3 and their expenses bear the ratio 3:2. Each of them saves Rs. 6,000 at the end of the month, then the monthly income of A is:

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A. Rs. 12,000

B. Rs. 24,000

C. Rs. 30,000

D. Rs. 60.000

E. Rs. 35,000

Explanation :

Let the monthly incomes of A and B be Rs. 4x and Rs. 3x respectively and their expenditures be Rs. 3y and Rs. 2y respectively.

4x – 3y = 6000 and 3x – 2y = 6000

⇒ 4x – 3y = 3x – 2y ⇒ x = y = 4x – 3y = 6000

⇒ x = 6000

⇒ A’s monthly income = 4x = Rs. 24000

573. The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers?

A. 15

B. 17

C. 19

D. 21

Explanation :

If the smallest number be x, then

x/3 + 12 = x + 2 ⇒ x + 36 = 3x + 6

⇒ 3x – x = 36 – 6 ⇒ 2x = 30 ⇒ x = 15

Third number = 15 + 4 = 19

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574. The total cost of 8 buckets and 5 mugs is Rs. 92 and the total cost of 5 buckets and 8 mugs is Rs. 77. Find the cost of 2 mugs and 3 buckets. A.

A. Rs. 35

B. Rs. 70

C. Rs. 30

D. Rs. 38

Explanation :

CP of 1 bucket = Rs. X

CP of 1 mug = Rs. Y

∴ 8x + 5y = 92………….. (i)

5x + 8y = 77 …………….(ii)

By equation (i) × 5 – equation (ii) × 8.

40x + 25y – 40x – 64y

= 460 – 616 ⇒ − 39y = - 156⇒ y = 4

From equation (i),

8x + 20 = 92 ⇒8x = 92 – 20 = 72 ⇒ x = 9

∴ CP of 2 mugs and 3 buckets

= 2 × 4 + 3 × 9 = 8 + 27 = Rs. 35

575. If a/(1-a) + b/(1-b) + c/(1-c) = 1 then the value of 1/(1-a) + 1/(1-b) + 1/(1-c) is:

A. 1

B. 3

C. 4

D. 0

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Explanation :

576. If 4x/3 + 2P = 12 for what value of P, x = 6?

A. 6

B. 4

C.

D. 1

Explanation :

When x = 6, (4 * 6)/3 + 2P = 12

⇒ 8 + 2P = 12

⇒ 2P = 12 – 8 = 4

⇒ P = 2

577. The value of (4+3√3)/(7+4√3) is:

A. 5√3 - 8

B. 5√3 + 8

C. 8√3 + 5

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D. 8√3 – 5

Explanation :

Expression = (4+3√3)/(7+4√3)

Rationalizing the denominator

578. A & B started a business together by investing Rs. 36000/- and Rs. 42000/- respectively. Both of them invested for one year whereas after 6 months from the start C joined them by investing a certain amount. If they earned an annual profit of Rs. 39,200/- out of which C’s share is Rs. 7350/-. What is the investment of C?

A. Rs. 24000/-

B. Rs. 36000/-

C. Rs. 27000/-

D. Rs. 33000/-

E. Rs. 30000/-

Explanation :

Let the investment of C=Rs x

Ratio of profits of A &B &C

=36000×12 : 42000×12 : x×6

=72000:84000: x

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Solving, x = 36000. B option.

579. What are the marks obtained by Harish in Maths ?

I. Average marks obtained by Harish in Maths and economies are 83.

II. Average marks obtained by Harish in Maths and statistics are 92.

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.

B. The data in both the statements I & II together are necessary to answer the question.

C. The data either in statement I alone or in statement II are sufficient to answer the question.

D. The data in both the statements I & II together are insufficient to answer the question.

E. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Explanation :

We cannot find the marks in maths alone even by using both the statements together as average marks will not tell us exact marks in Maths.

Data is insufficient. Hence D option.

580. By what percent is Rajesh’s salary more/less than Mangesh’s ?

I. Salary of Rajesh is Rs. 12000/-.

II. Salary of Rajesh and Mangesh together is Rs 28000/-.

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.

B. The data in both the statements I & II together are necessary to answer the question.

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C. The data either in statement I alone or in statement II are sufficient to answer the question.

D. The data in both the statements I & II together are insufficient to answer the question.

E. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Explanation :

By using both the statements together we can find the salary of Mangesh . Hence we can find the percentage change between the salaries of Rajesh and Mangesh. B option.

581. What is the strength of MBA institute where students study only HR, Marketing and Finance ?

I. Number of students studying HR, Marketing and Financial are in the ratio of 2 : 3: 5 respectively.

II. Number of students studying Marketing is more than those studying HR by 800. Answer: Choice No. C.

A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

B. The data either in statement I alone or in statement II alone are sufficient to answer the question.

C. The data in both the statements I & II together are necessary to answer the question.

D. The data in statement II alone are sufficient to answer the question, while the data in statement I alone not sufficient to answer the question.

E. The data in both the statements I & II together are insufficient to answer the question.

Explanation :

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Using both statements together , Let no. of students of HR, marketing and Finance be 2x,3x,5x and also 3x-2x=800

x=800

So total students =2x+3x+5x=10×800=8000. Hence C.

582. A shopkeeper purchased 96 identical shirts @ Rs. 220/- each. He spent Rs. 3800/- on transport and packing and fixed a marked price of Rs. 450/- each shirt. However, he decided to give discount of 20% on the marked price of each shirt. If he could sell all the shirts, what is the approximate percent profit earned by him?

A. 44

B. 39

C. 33

D. 31

E. 30

Explanation :

Cost of 96 shirts=Rs96×220=Rs.21120

Cost of transportation and packaging =Rs3800

Total Cost price (CP)

=Rs 3800+21120 = Rs24920

Marked Price (MP) of 1 shirt =Rs.450

Discount=20% of Rs450

Net Selling Price (SP) of 1 shirt

=80% of Rs450 = Rs360

Total SP of 96 shirts =Rs 360×96=Rs.34560

Profit Percentage = (SP - CP)/CP * 100%

(34560 - 24920)/24920 * 100% = 38.68% = 39%. Hence, option B.

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583. Type A, 12 kg of rice worth Rs. 40/kg is mixed with Type B, rice worth Rs. 24/kg. What should be the quantity of Type B rice, if the mixture is sold at Rs. 45/kg with 25% profit added in it?

A. 18 Kg

B. 48 Kg

C. 4 Kg

D. can't say

Explanation :

C.P. of the mixture = 45/1.25 = Rs. 36/kg.

So, (40-36)/(36-24) = (N)/(12) ⇒ N = 4 Kg

584. A person spends 1/7th of his salary on travel,1/3rd of the remaining on food, he then spends 1/4th of the remaining on rent. Finally he puts 1/6th of the remaining as a monthly savings, after which he has 25000 left. What is his salary (in Rs.)?

A. 70,000

B. 14,000

C. 84,000

D. 26,000

Explanation :

Let M be the total salary

Therefore, as per question, M × (6/7) × (2/3) × (3/4) × (5/6) = Rs 25000

M = Rs 70000

585. Point C(x,y) divides the distance AB with point A(8,12) and point B(16, 18) in a ratio of 3:5, with AC being shorter than BC. What are the co-ordinates of C?

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A. (12,15)

B. (14.5, 12.5)

C. (14.5, 12.5)

D. (11,14.25)

Explanation :

x co-ordinate of C = [(5×8) + (3×16)] / (3+5) = 11

y co-ordinate of C = [(5×12) + (3×18)] / (3+5) = 14.25

Co-ordinates of C is ( 11, 14.25 )

586. How many terms of the sequence -12, -8, -4,…so on, to make a sum of 120?

A. 11

B. 12

C. 10

D. 13

Explanation :

The series is in A.P. where a = -12 and d = 4.

So 120 = (n/2)[2 × (-12) + (n -1) × 4].

On solving this, we get n = 12

587. The value of a machine depreciates from Rs 32,768 to Rs 21,952 in three years. What is the rate % of depreciation?

A. 11%

B. 12.25%

C. 12.5%

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D. 33%

Explanation :

Let R be the rate of depriciation, therefore, 21952 = 32768[1-(R/100)]3 . On solving this we get R = 12.5%

588. A TV set listed at Rs 3200 is sold to a retailer at a successive discount of 25% and 15%. The retailer desires a profit of 20%, after allowing a discount of 10% to the customer. At what price should he list the TV set (in Rs.)?

A. 2720

B. 2448

C. 2040

D. 2133

Explanation :

The retailers C.P. = 3200 × 0.75 × 0.85 = Rs 2040.

His expected S.P. = 2040 × 1.2 = Rs 2448.

But S.P. is 90% of the L.P., as there is a discount of 10%.

So L.P. = 2448/0.9 = Rs 2720

589. A student is to answer 10 out of 12 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A. 140

B. 280

C. 196

D. 346

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Explanation :

4 questions can be chosen from the first 5 in 5 ways. Remaining 6 questions can be selected from 8 questions in 8C6 ways. So required answer is 8C6 × 5 = 28 × 5 = 140.

590. A rectangular playground with the dimension of 50m X 30 m is surrounded by a 5 m wide road all the sides. What is the area of the road?

A. 600 sq. m.

B. 500 sq. m.

C. 450 sq. m.

D. 900 sq. m.

Explanation :

AREA OF ROAD= area of bigger rectangle - area of smaller rectangle ⇒(60×40)-(50×30)⇒2400-1500=900.

591. It takes 5 sec. for a clock to strike at 5’o clock. If the striking intervals are uniform how much time will it take to strike 9’o clock (in sec.)?

A. 9

B. 10

C. 11

D. 12

Explanation :

There are 4 intervals in 5 strokes.

Time taken to strike 1 stroke will be 5/4 sec.

At 9, there will be 9 strokes and 8 intervals between two strokes.

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Thus time required = 5/4 × 8 = 10 sec

592. From the top of the Tower which is 240m high, if the angle of depression of a point on the ground is 30°, then the distance of the point from the foot of the Tower is

A. 40 √ 3

B. 80 √ 3

C. 120 √ 3

D. 240 √ 3

Explanation :

593. At the start of a seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break, 16 participants left and 6 more female participants registered. The ratio of the male to the female participants became 2:1. The total number of participants at the start of the seminar was -

A. 64

B. 48

C. 54

D. Data Insufficient.

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Explanation :

In this question, as per the information given we cannot determine how many are males and how many are females out of 16 participants who left. So, data is insufficient to answer the given question.

594. A man can row 30 km upstream and 44 km downstream in 10 hours. Also, he can row 40 km upstream and 55 km downstream in 13 hours. The rate of the current is -

A. 3 km/hr

B. 3.5 km/hr

C. 4 km/hr

D. 4.5 km/hr

Explanation :

Let the speed of the man in still water be x km/hr and speed of the stream be y km/h then

Solving (i) and (ii) x = 8 km/hr and y = 3 km/hr

So the rate of stream is 3km/hr.

595. There are two identical vessels, X and Y. Y is filled with water to the brim and X is empty. There are two pails A and B, such that B can hold half as much water as A. One operation is said to be executed when water is transferred from Y to X using A once and water is transferred to Y from X using B once. If A can hold a liter of water and it takes 40 operations to equate the water level in X and Y, what is the total volume of water in the system

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A. 10 liters

B. 20 liters

C. 40 liters

D. 203⁄4 liters

Explanation :

In one complete operation, water transferred = 1 - (1/2) = 1/2 liters as 1 liter goes from Y to X. So 1 liter is contained in X. But ½ liter goes from X to Y as well. So net ½ liters remain in X. If it takes 40 operations to equate water level,

∴ 40 × (1/2) = 20 liters is contained in X and Y.

Hence total volume of water in the system is 40 litres. Hence, 3rd option.

596. A salesman's terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs. 1,000 plus 2.5 % commission on all sales exceeding Rs. 4,000. If his remuneration as per the new scheme was Rs. 600 more than by the first scheme, what were his sales worth

A. Rs. 11, 000

B. Rs. 17, 000

C. Rs. 16, 000

D. Rs. 12, 000

Explanation :

Let his sales were worth Rs. x.

So as per the question,

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597. In a class with a certain number of students if one student weighing 50 kg is added then the average weight of the class increases by 1 kg. If one more student weighing 50 kg is added then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?

A. 46

B. 4

C. 2

D. 47

Explanation :

Let x be the original average and n be the number of students. Let x1, x2, x3 ,. . . .. xn be the weights of n students respectively. Therefore,

x1, x2, x3 ,. . . .. xn / n = x

x1, x2, x3 ,. . . .. xn = nx...............(1)

Now,according to 1st condition we have

x1, x2, x3 ,. . . .. xn + 50/ n+1 = x+1

x1, x2, x3 ,. . . .. xn = (n+1)(x+1) - 50..............(2)

Further,according to 2nd condition we have

x1, x2, x3 ,. . . .. xn + 50+50/ n+2 = x+1.5

x1, x2, x3 ,. . . .. xn = (n+2)(x+1.5) - 100..............(3)

Solving (1) and (2), we get

x + n = 49…………….. (4)

Solving (1) and (3), we get

4x + 3n = 194 ……………. (5)

Now, Solving (4) and (5), we get

n = 2, x = 47

So, the original average weight (in kg) of the class = 47

Alternate Solution :

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Let x be the original average and n be the number of students.

From the first increase in the average,

we get 50 – x = n + 1

From the second increase in the average,

we get 100 – 2x = 1.5 (n + 2)

Solving, we get the value of x = 47.

598. The average marks of a student in 8 subjects is 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated, the average marks of the remaining subjects are 85. What are the highest marks obtained by him

A. 94

B. 91

C. 89

D. 96

Explanation :

Let highest marks be (x +2), So, next score = x Total of 8 subjects = 8 × 87 = 696

So, As per question, 696 - x = (x+2) / 6 =85

⇒ x = 92 So, highest marks = (x + 2) = 92 + 2 = 94.

599. If a bucket is 80% full, then it contains 2 liters more water than when it is 662/3% full. What is the capacity of the bucket?

A. 10 liters

B. 15 liters

C. 162/3 liters

D. 20 liters

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Explanation :

Let the capacity of bucket is x litre.

As per the question,

we have [(4x)/5 - (2x)/3] = 2

⇒ x = 15 litres.

600. The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Rs. 1,800. In another month 620 units are consumed and the bill is Rs. 2,040. In yet another month 500 units are consumed. The bill for that month would be

A. Rs. 1,560

B. Rs. 1,680

C. Rs. 1,840

D. Rs. 1,950

Explanation :

Let V be the variable part of the bill and F be the fixed part. Given 540V + F = 1800 & 620 V + F = 2040. Solving these we get V = 3 and F = 180. So when 500 units are consumed, 500V + F = 500 × 3 + 180 = Rs. 1680.

601. Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/sec and 8 m/sec respectively. If the circumference of the circle is 300 metres, after what time will they meet at the starting point for the first time

A. 20 sec

B. 100 sec

C. 300 sec

D. 200 sec

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Explanation :

S = D/T The times taken by the two cyclists to reach the starting point are 300/7 seconds and 300/8 seconds respectively. So, they will meet at the starting point after LCM(300/7, 300/8) = 300 seconds.

602. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?

A. 76.5 Kg

B. 78 Kg

C. 85 Kg

Explanation :

Increase of Average = 2.5 for 8 persons

Total Increase = 2.5 × 8 = 20 kg.

Weight of New Person = 65 kg + 20 kg = 85 kg

603. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A. 1520 sqm

B. 2520 sqm

C. 2480 sqm

D. 2720 sqm

Explanation :

P = 2 (L + B) L – B = 23

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=> 2 L + 2 B = 206

2 L – 2 B = 46

=> L = 63;

B = 40 Area = 63 × 40 = 2520 sqm

604. On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?

A. Sunday

B. Monday

C. Tuesday

D. Thursday

Explanation :

Between 8th February 2004 & 8th Feb 2005 there are 366 days.

366 days => 52 weeks + 2 days

Hence, it was SUNDAY

605. In one hour, a boat goes 11 km/hour along the stream and 5 km/hour against the stream. The speed of the boat in still water (in km/hour) is:

A. 5

B. 7

C. 8

D. 10

Explanation :

11/(B+S) = 1 hr

5/(B-S) = 1 hr

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=> B + S = 11 & B - S = 5

Therefore, on solving we get

= > Boat speed = 8km/hr

Stream Speed = 3km/hr

606. Ram purchased 20 dozens of toys at the rate of Rs.375 per dozen. He sold each one of them at the rate of Rs.33. What was his percentage profit?

A. 3.6

B. 3.8

C. 4.1

D. 5.6

Explanation :

CP = 375 × 20 = 7500/-

SP = 33 × 12 × 20 = 7920/-

Therefore, % Profit = (7920 - 7500)/7500 × 100 = 5.6%

607. When the profit on a commodity triples then its selling price is doubled. Find the profit percent.

A. 35

B. 50

C. 85

D. 100

Explanation :

Going by the options (d) satisfies

CP = 100/- Price = 100% SP = 200/-

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CP = 100/- Price = 300% SP = 400/-

608. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

A. 4m

B. 6m

C. 8m

D. 9m

Explanation :

A -> runs 100m

B -> runs 90m

C -> runs 87m

=> B runs 180m

C runs 174 m => 6m

609. A dishonest milk seller professes to sell the milk at cost price but gain 20%. The proportion of milk and water is:

A. 5:3

B. 4:1

C. 6:5

D. 5:1

Explanation :

The amount of water is the Gain ( 20% )

=> Proportion is 4: 1

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610. It takes 5 hours for a boat to go down-stream and 10 hours to return to the same place against the stream. If the stream is flowing at the rate of 40 km/hour, calculate the speed of the boat.

A. 150 km/hour

B. 170 km/hour

C. 120 km/hour

D. 100 km/hour

Explanation :

D/(B - 40) = 5 hr

D/(B + 40) = 10 hr

=> B - 40 = 5/D & B - 40 = 10/D

=> 2B - 80 = B + 40

Therefore, speed of boat = 120 km/hr

611. Cost price of 30 mangoes is equal to the selling price of 24 mangoes. Calculate the percentage of profit.

A. 20

B. 25

C. 30

D. 32

Explanation :

CP of 1 Mango = 1/-

CP of 30 Mango = 30/-

SP of 24 Mangoes = 30/-

SP of 1 Mango = 1.25/-

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=> Profit = 25%

612. A cricketer played 80 innings and scored an average of 99 runs. His score in the last inning was zero run. To have an average of 100 at the end, his score in the last innings should have been

A. 60

B. 80

C. 10

D. 1

E. None of these

Explanation :

Let x be the score in the last inning to make the average of 100

Therefore, when average is 99, total score of 80 innings = 80 * 99 = 7920

And when the average is 100, total score of 80 innings = 80 * 100 = 8000

Therefore, x = 8000 - 7920 = 80

613. A man spends an average of Rs. 1,694.70 per month for the first 7 months and Rs.1,810.50 per month for the next 5 months. His monthly salary if he saves Rs. 3,084.60 during the whole year is

A. 1000

B. 2000

C. 2400

D. 3000

E. None of these

Explanation :

Monthly salary =

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614. A and B undertake to do a piece of work for Rs. 2,200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days. Find C's share.

A. 150

B. 275

C. 245

D. 175

E. None of these

Explanation :

Let 1 be the total work

Therefore, C's one day work = (1/3)-[(1/8)+(1/6)]= 1/24

Ratio of share of A, B and C

i.e. A:B:C = 1/8:1/6:1/24=> [1/3] - {[1/8]+[1/6]} = (1/24) 3 : 4 : 1

So, C's share = {1/8} *2200=275-/

615. By selling an article at 80% of its marked price, a trader makes a loss of 10%. What will be the profit percentage if he sells it at 95% of its marked price?

A. 5.9

B. 12.5

C. 6.9

D. 5

E. None of these

Explanation :

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Let us assume the MP to be 900/-

Therefore, SP = 80% of MP = 0.80 * 900 = 720/-

As loss is 10%, so CP = 720/90 *100=800

Now, if SP = 95% of MP = 0.95 *900 = 855/-

Profit% = 855-800 /800 =55/8=6.9

616. By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% of the marked price. His gain during the sale season is

A. 8

B. 9

C. 7

D. 7.5

E. None of these

Explanation :

Given that SP of umbrella = 30/- and profit% = 20. Therefore, CP of umbrella = 30/120 *100=25 SP of umbrella after 10% discount = 90/100 *30=27 Thus, profit% = 27-25 /25 =8

617. From a vessel containing 100 ltr. of wine, 10 ltr. are drawn out and an equal amount of water is added. From the mixture, 10 ltr. is again drawn out and same quantity of water is added. What is the final ratio of wine and water?

A. 91:9

B. 81:19

C. 80:20

D. 90:10

E. None of these

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Explanation :

This is the question of removal and replacement If a vessel contains "x" litres of liquid A and if "y" litres be withdrawn and replaced by liquid B, then if "y" litres of the mixture be withdrawn and replaced by liquid B again, and the operation is repeated "n" times in all, then:

So, in the given question, we have A as wine and B as water and 2 operations have occurred.

Therefore, quantity of wine after 2 operations

Thus, in a mixture of 100 ltr, 81 is wine, so water will be 100 - 81 = 19 ltr

Required ratio of wine and water is 81 : 19

618. From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?

A. 4:1

B. 4:2

C. 5:2

D. 1:4

E. None of these

Explanation :

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619. Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages per person are in the proportion of 5 : 3 : 2. When 90 men are employed, total daily wages of all amounts to Rs. 10,350. Find the daily wage of a man.

A. 115

B. 75

C. 45

D. 57.90

E. None of these

Explanation :

Let the daily wages be 5k, 3k and 2k of men, women and children respectively.

We are given that there are 90 men and total amount of wages is 10350/-

Thus, men, women and children are 90, 60 and 30 respectively.

Hence, total wages = 90 x 5k + 60 x 3k + 30 x 2k = 10350

=>k = Rs.15

Thus, daily wages of each man = 5k = Rs.15 x 5 = Rs. 75

620. The population of a town is 3,11,250. The ratio between women and men is 43 : 40. If there are 24% literate among men and 8% literate among women, the total number of literate persons in the town is

A. 56,800

B. 99,600

C. 41,800

D. 48,900

E. None of these

Explanation :

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Total number of literate people is 24 % of 40 % of men and 8 % of 43 % of women.

Therefore, No of literate persons = [24/100 *40/83* 311250 ] + [ 8/100 * 43/83 * 311250] = 48900

621. In an examination, 52% of the candidates failed in English and 43% failed in Mathematics. If 17% failed in both the subjects, then the percentage of candidates, who passed in both the subjects, was

A. 25

B. 22

C. 23

D. 21

E. None of The above

Explanation :

% of students failed in Mathematics only = 43% – 17% = 26%

% of students failed in English only = 52% – 17% = 35%. So % of students passed in both = 100 – (26 + 35 + 17) = 100 – 78 = 22% Alternate Solution:

% of students failed in Mathematics or English or both = 52% + 43% – 17% = 78%

So % of students passed in both = 100% – 78% = 22%. Hence, option B is correct.

622. Suri gave 25% of her monthly salary to her mother. From the remaining salary, she paid 15% towards rent and 25%, she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 42000. What was her monthly salary?

A. Rs. 50,000

B. Rs. 60,000

C. Rs. 65,000

D. Rs. 64,000

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E. Rs. 72,000

Explanation :

Let x be the total income

(75/100*60/100)x + 25/100x = 42000

Solving, x = 60000

623. Type A, 12 kg of rice worth Rs. 40/kg is mixed with Type B, rice worth Rs. 24/kg. What should be the quantity of Type B rice, if the mixture is sold at Rs. 45/kg with 25% profit added in it?

A. 18 kg

B. 48 kg

C. 4 kg

D. can't say

Explanation :

C.P. of the mixture = 45/1.25 = Rs. 36/kg.

So, (40-36)/(36-24) = (N)/(12) ⇒ N = 4 Kg

624. A person spends 1/7th of his salary on travel,1/3rd of the remaining on food, he then spends 1/4th of the remaining on rent. Finally he puts 1/6th of the remaining as a monthly savings, after which he has 25000 left. What is his salary (in Rs.)?

A. 70,000

B. 14,000

C. 84,000

D. 26,000

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Explanation :

Let M be the total salary

Therefore, as per question, M × (6/7) × (2/3) × (3/4) × (5/6) = Rs 25000

M = Rs 70000

625. A TV set listed at Rs 3200 is sold to a retailer at a successive discount of 25% and 15%. The retailer desires a profit of 20%, after allowing a discount of 10% to the customer. At what price should he list the TV set (in Rs.)?

A. 2720

B. 2448

C. 2040

E. 2133

Explanation :

The retailers C.P. = 3200 × 0.75 × 0.85 = Rs 2040

. His expected S.P. = 2040 × 1.2 = Rs 2448.

But S.P. is 90% of the L.P., as there is a discount of 10%.

So L.P. = 2448/0.9 = Rs 2720

626. A student is to answer 10 out of 12 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A. 140

B. 280

C. 196

D. 346

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Explanation :

4 questions can be chosen from the first 5 in 5 ways. Remaining 6 questions can be selected from 8 questions in 8C6ways. So required answer is 8C6 × 5 = 28 × 5 = 140.

627. 6. Two years ago the average age of a family of 8 members was 18 years. After the addition of a baby, the average age of family remains the same today. What is the age of the baby ?

A. 1 year

B. 2 years

C. 4 years

D. 3.5 years

628. An article when sold at a gain of 5% yields Rs. 15 more than when sold at a loss of 5%. The cost price of the article is:

A. Rs. 200

B. Rs. 150

C. Rs. 80

D. Rs. 64

Explanation :

10/100 × x = 15 ⇒ x=150

As the loss and profit both are earned on the cost price.

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629. The tax on a commodity is diminished by 10 % and its consumption increased by 10 %. The effect on the revenue derived from it changes by K %. Find the value of K.

A. 1

B. -2

C. -1

D. 2

Explanation :

Directly using the formula, when a value is increased by R% and then decreased by R%, then net there is ( R^2)/100 decrease. Putting R = 10, we get 1% decrease.

630. Ratio of Ashok's age to Pradeep's age is 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now?

A. 18

B. 21

C. 15

D. 24

Explanation :

Given A/p= 4/3 Also A = 26 after 6 years, so his present age = 20years, Substituting we get P = 15 years.

631. The incomes of Chanda and Kim are in the ratio 9 : 4 and their expenditures are in the ratio 7 : 3. If each saves Rs. 2,000, then Chanda's expenditure is

A. 60000

B. 80000

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C. 70000

D. None of these

Explanation :

Let the incomes of Chanda and Kim be 9x and expenditures be 7y and 3y respectively. Since = Income – Expenditure, we get 9x – 7y = 2000 and 4x – 3y = 2000. Solving, we get, x = 8000 and y = 10000. So Chanda’s expenditure = 7y = 7 × 10000 = Rs. 70,000.

632. 7 cannibals of XYZ island, decide to throw a party. As you may be aware, cannibals are guys who eat human beings. The senior among them – Father Cannibal decides that any 6 of them will eat up one cannibal, and then out of the remaining six – five of them will eat up one cannibal and so on till one is left. What is the time until one cannibal is left, if it takes one cannibal 3 hours to eat up one cannibal independently?

A. 7 hrs 11 min

B. 6 hrs 12 min

C. 7 hrs 21 min

D. 18 hrs 16 min

Explanation :

At the beginning 6 cannibals will eat one, so time required will be 180/6 = 30 min.

Then out of the remaining six – five will devour one, so time required will be 180/5 = 36 min.

Thus the time until one cannibal is left will be = (180/6 + 180/5 + 180/4 + 180/3 + 180/2 + 180/1) min

= (30 + 36 + 45 + 60 + 90 + 180) min

= 441 min

= 7 hrs 21 min.

Hence option 3.

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633. Three articles are purchased for Rs. 1050, each with a different cost. The first article was sold at a loss of 20%, the second at 1/3rd

A. 14.28% gain

B. 13% loss

C. 12% loss

D. 11.11% gain

Explanation :

Let us assume that their CPs are x, y & z respectively.

According to the given condition 0.8x = 1.33y = 1.6z

⇒ (80/100)x = 400y/(3 × 100) = (160/100)z

⇒ x : y = 5 : 3 & y : z = 6 : 5

Thus x : y : z = 10 : 6 : 5

Hence CPs of the articles are x = (10/21) × 1050 = 500,

y = (6/21) × 1050 = 300 &

z = (5/21) × 1050 = 250.

SP of the article with CP Rs. x is 0.8x = 0.8 × 500 = 400.

Since SPs are same, the total SP will be 400 × 3 = 1200.

Hence the gain % = (SP – CP)/CP × 100 = (1200 – 1050)/1050 × 100 = 14.28%.

634. In a game of tennis, A gives B 21 points and gives C 25 points. B gives C 10 points. How many points make the game?

A. 50

B. 45

C. 35

D. 30

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Explanation :

When B scored p -10 then C scored p - 25.

When B scores 1 then C scores (p-25)/(p-10)

So when B scores p points then C will score (p-25)/(p-10) × p

As per question (p-25)/(p-10) × p = p -10 . Solving this we get p = 35

A B C

p points (p-21)points (p-25)points

p points (p-10)points

635. Twice the speed of a boat downstream is equal to thrice the speed upstream. The ratio of its speed in still water to the speed of current is

A. 1 : 5

B. 1 : 3

C. 5 : 1

E. 2 : 3

Explanation :

Let the boat speed in still water be b.

Let the stream speed be x.

2(b+ x) = 3(b-x)

5x=b

b/x=5/1

636. A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed with that chemical so that after selling the mixture at Rs. 20/litre he may get a profit of 25%?

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A. 13 : 16

B. 12 : 15

C. 9 : 16

D. 19 : 22

Explanation :

This can be solved using allegation.

What is required at the end of mixing is a price of 20/1.25 = 16.

So the allegation would look like this –

Hence the ratio would be (25 – 16) : 16 = 9 : 16

Hence required ratio of Water : Chemical is 9:16.

637. The difference between the simple interest and compound interest on a certain sum of money for 2 years at 15% p. a. is Rs. 45. Find the sum.

A. Rs. 2700

B. Rs. 2500

C. Rs. 2000

D. None of these

Explanation :

Since we know that the interest rate is 0.15, and knowing that the difference between two years of compound interest is nothing but interest on interest, we can find the first year’s interest as –

45/0.15 = 300.

Now if the interest is 300 at the end of one year, then the principal is 300 / 0.15 = 2,000.

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638. How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively, and the sum of terms is 40?

A. 15

B. 10

C. 5

D. 20

Explanation :

Now the common difference of this AP is 16/4 = 4.

The sum of an AP is n/2 {2a + (n – 1)d}

Substituting we get, 40 = n/2 {2×-14 + (n – 1)4}

The best way to solve this is by plugging options. Put in n = 10 and get the RHS as 40.

639. The difference of two numbers is 11 and one fifth of their sum is 9. The numbers are :

A. 31, 20

B. 30, 19

C. 29, 18

D. 28, 17

Explanation :

x − y = 11, x + y = 5 × 9 x − y = 11, x + y = 45, y = 17, x = 28

640. How many numbers between 1 and 100 are divisible by 7?

A. 9

B. 11

C. 17

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D. 14

Explanation :

No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d

98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7

98/7= N = 14

641. What is the number which when multiplied by 13 is increased by 180?

A. 13

B. 15

C. 23

D. 35

Explanation :

13 × 15 = 195

642. In 24 minutes, the hour hand of a clock moves through an angle of:

A. 60°

B. 24°

C. 12°

D. 5°

Explanation :

12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚

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643. √0.0081 is equal to :

A. 0.09

B. 0.9

C. ±0.08

D. 0.81

Explanation :

√0.0081 = √0.0081/10000 = √81/10000 = 9/100 =0.09

644. A reduction of 20% in the price of mangoes enables a person to purchase 12 more for Rs. 15. What was the price of 16 mangoes before reduction of price?

A. Rs. 6

B. Rs. 5

C. Rs. 7

D. Rs. 9

Explanation :

645. The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age?

A. 30 years

B. 38 years

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C. 44 years

D. 42 years

Explanation :

Total sum of man's age & his son's age =28 × 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man's age = (3/4) × 56 = 42

So, the correct answer is option D.

646. A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC.

A. θ

B. θ/2

C. 2θ

D. 3θ

Explanation :

∠B + ∠D = 180° ∠A + ∠C = 180° ∠BAC = ∠BCA ∠DAC = ∠DCA ∴∠DAB = ∠DCB = 90° ∠DAC = θ

∴∠ADE = 90° - θ = ∠CDE ∴ ∠ABC = 180° – 2(90° - θ) = 2θ

647. How many integers are there between 300 and 600 that are divisible by 9?

A. 33

B. 31

C. 28

D. 25

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Explanation :

The sequence is 306… 594

594=306+ (n-1)9⇒288= (n-1)9⇒n=33

648. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1,5:2 and 6:1 respectively?

A. 166 : 22

B. 83 : 22

C. 83 : 44

D. 78 : 55

E. None of these

Explanation :

Three identical vessels in the ratio 4:1, 5:2 and 6 :1 respectively.

Petrol : kerosene

(4 : 1 = 5)7

(5 : 2 = 7)5

(6 : 1 = 7)5

28 : 7 = 35

25 : 10 = 35

30 : 5 = 35

83 : 22

649. There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number?

A. 31

B. 27

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C. 29

D. 25

E. 33

Explanation :

Let the 6 consecutive odd no.’s are:

X, X+2, X+4, X+6, X+8, X+10

Avg. of 1st three no’s is X+2.

Avg. of Last three no’s is X+8.

X=19

Last Odd no. is X+10= 29.

650. In a bag there are 6 red balls and 9 green balls. Two balls are drawn at random, what is the probability that at least one of the balls drawn is red?

A. 29/35

B. 7/15

C. 23/35

D. 2/5

E. 19/35

Explanation :

Probability of atleast one of the balls drawn is red= 1- (9/15) * (8/14)=23/35.

651. A started a business with an investment of Rs. 28,000. After 5 months from the start of the business, B and C joined with Rs. 24,000and Rs. 32,000

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respectively and withdrew Rs. 8000 from the business. If the difference between A’s share and B’s share in the annual profit is Rs. 2,400, what was the annual profit received?

A. Rs. 15,600

B. Rs. 14,400

C. Rs. 14,040

D. Rs. 15,360

E. Rs. 13,440

Explanation :

Equivalent Contribution of A= 28000 * 5+20000 * 7= 280000

Equivalent Contribution of B= 24000 * 7= 168000

Equivalent Contribution of C= 32000 * 7= 224000

Let total profit be X.

Given that,

280000X/672000 – 168000X/672000=2400

112000/672000 * X=2400

or X=2400 * 672/112

X=14400

652. At present, Ami’s age is twice Dio’s age and Cami is two years older than Ami. Two years ago, the respective ratio between Dio’s age at that time and Cami’s age at that time was 4 : 9. What will be Ami’s age four years hence?

A. 40 years

B. 30 years

C. 42 years

D. 36 years

E. 48 years

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Explanation :

A = 2D; C = A+2 = 2D+2

Given, D-2/(2D+2)-2 = 4/9

Solving, D = 18 Years and A = 36+4 = 40 years.

653. Three Science classes A, B and C take a Life Science test. The average score of students of class A is83. The average score of students class B is 76. The average score of class C is 85. The average score of class A and 8 is 79 and average score of class B and C is 81. Then the average score. Of classes A, B and C is

A. 80

B. 80.5

C. 81

D. 81.5

E. None of these

Explanation :

T.I.=30,000, N.T.I.=18000

Taxable 12000, Income Tax = 25% of Taxable Income

= 1/4 ×: 12000 = RS.3000

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A:B:C = 3:4:5

Sum of A+B+C = 3*83+4*76+5*85 = 978

Average score = 978/12 = 81.5

654. A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?

A. 221

B. 343

C. 81

D. 243

E. None of these

Explanation :

Area of a hemispherical bowl = 2/3 ×π ×r3

Area of a cylinder = πr2h

Area of a cylinder = n × Area of a hemispherical bowl

2/3 ×π ×273 = n ×π×32×9

we get n = 162

DIRECTIONS for the questions 655 & 657 : What approximate value will come in place of question mark (?) in the given question?( You are not expected to calculate the exact value.)

655. 26.00 - 154.001/6.995 = ?

A. 4

B. 18

C. 9

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D. 10

E. 14

Explanation :

26 – (154/7) = 4

656. 17.995/3.01 + 104.001/12.999 = ?

A. 11

B. 20

C. 23

D. 14

E. 17

Explanation :

18/3 + 104/13 = 14

657. 3/5 of 4/7 of 7/9 of 425 = ?

A. 121

B. 110

C. 118

D. 113

E. 124

Explanation :

3/5*4/7*7/9*425 = 113

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658. If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be :

A. 128

B. 132

C. 133

D. 136

Explanation :

If values are proportional to 13 : 11 : 7, then the number of coins will be proportional to 13/1 : 11/0.50 : 7/0.25

⇒ 13 : 22 : 28. Now from this the number of coins of 50 paise will be 378 × 22/63 = 132.

659. How many words, with or without meaning can be formed with the letters of the word MANAGEMENT?

A. 226800

B. 453600

C. 3907200

D. 1814400

E. 3628800

Explanation :

Reqd. number of ways = (10!/2!2!2!2!)=226800

660. The number of ways in which letters of the word PRAISE be arranged

A. 720

B. 610

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C. 360

D. 210

E. None of these

Explanation :

Reqd. number of ways = 6! = 720.

661. Jar A has 60 litres of mixture of milk and water in the respective ratio of 2: 1. Jar B which had 40 litres of mixture of milk and water was emptied into Jar A, as a result in Jar A, the respective ratio of milk and water becomes 13 : 7. What was the quantity of water in Jar B?

A. 8 litres

B. 15 litres

C. 22 litres

D. 7 litres

E. 1 litres

Explanation :

Jar A has 60 Litres.

Ratio between milk and water 2:1,

Quantity of Milk in Jar A = 2/3×60 = 40

Quantity of Water in Jar A = 1/3× 60 = 20

40 liters of Mixture B having milk and water is emptied into Jar A.

Therefore, Total Mixture = 60 +40 = 100

The respective Ratio of Milk and Water is 13:7

Quantity of Milk in Jar A = (13/20)×100 = 65

Quantity of Water in Jar A = (7/15)× 100 = 35

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Quantity of water in Jar B = 35 – 20 = 15 Litres.

662. The sum of a series of 5 consecutive odd numbers is 195. The second lowest number of this series is one less than the second highest number of another series of 5 consecutive even numbers. What is 40% of the second lowest number of the series of consecutive even numbers?

A. 16.8

B. 14.8

C. 19.4

D. 17.6

E. 13.6

Explanation :

The sum of a series of 5 Consecutive odd numbers is 195

Let the Series of Consecutive odd numbers is X, X+2, X+4, X+6, X+8

X+ X+2+ X+4+ X+6+ X+8= 195

5X+20=195

X=35

Series of Consecutive odd numbers is 35, 37, 39, 41, 43

According to the question, the second lowest number of this series is 1 less than the Second highest number of another series of 5 consecutive numbers.

Second lowest number is 37.

Second highest number of another series of 5 consecutive numbers = 37+1 = 38

Therefore, another series of 5 consecutive numbers 32, 34, 36, 38, 40.

40% of the lowest number of the series of consecutive numbers= 34×(4/100) = 13.6

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663. The sum of the dimensions of a room (i.e. length, breadth and height) is 18 metres and its length, breadth and height are in the ratio of 3 : 2 : 1 respectively. If the room is to be painted at the rate of Rs. 15 per m2, what would be the total cost incurred on painting only the four walls of the room (in Rs.)?

A. 3250

B. 2445

C. 1350

D. 2210

E. 2940

Explanation :

Ratio of length : breadth : height = 3:2:1

Sum of dimensions of room = 18

Length =(3/6) ×18 = 9

Breath =(2/6) ×18 = 6

Height =(1/6) ×18 = 3

Area of four walls = 2h×(l+b) = 2×3(9+6) = 90

Total cost of painting four walls = 90×15 = 1350

664. B is 4/3 times as efficient as A. If A can complete 5/8th of a given task in 15 days, what fraction of the same task would remain incomplete if B works on it independently for 10 days only?

A. 3/4

B. 2/3

C. 5/8

D. 4/9

E. 2/3

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Explanation :

B is 4/3 times as efficient of A.

Ratio of time taken by A and B, A: B is 4:3.

A can complete 5/8th of a given task in 15 days

A can do alone his work in = 8/5×15= 24 days

Therefore, B can do this work= 18

B works independently for 10 days only, thus work done = 10/18 = 5/9

Remaining work (incomplete) = 1-(5/9) = 4/9

665. In a class, the average weight of boys is 64 kg and that of 75 girls is 70 kg. After a few days, 60% of the girls and 30% of the boys leave. What would be the new average weight of the class (in kg)? Assume that the average weight of the boys and the girls remain constant throughout.

A. 63

B. 66.5

C. 68.5

D. 65.5

E. Can’t be determined

Explanation :

In this question, number of boys is not mentioned .So, we can’t find new average.

DIRECTIONS for question 666 to 668: What will come in place of question mark (?) in the given number series?

666. 15 27 37 45 51 ?

A. 58

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B. 80

C. 65

D. 74

E. 55

Explanation :

Given series is:

15 27 37 45 51 ?

And the pattern is 27 – 15 = 12, 37 – 27 = 10, 45 – 37 = 8, 51 – 45 = 6.

Thus the next term is 51 + 4 = 55

667. 700 457 376 349 340 ?

A. 266

B. 329

C. 304

D. 337

E. 307

Explanation :

Given series is:

700 457 376 349 340 ?

Pattern is 700 – 457 = 243, 457 – 376 = 81, 376 – 349 = 27, 349 – 340 = 9

Thus, the next term is 340 – 3 = 337

668. 1 2 6 21 88 ?

A. 425

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B. 475

C. 295

D. 445

E. 395

Explanation :

Given series is:

1 2 6 21 88 ?

Pattern is 1×1+1= 2

2×2+2= 6

6×3+3=21

21×4+4= 88

88×5+5= 445

So the next term of the series is = 445

669. A 180-metre-long train crosses a platform of equal length in 18 seconds. What is the speed of the train?

A. 22m/sec

B. 10m/sec

C. 15m/sec

D. 18m/sec

E. None of these

Explanation :

At the beginning 6 cannibals will eat one, so time required will be 180/6 = 30 min.

When the train crosses the platform , it covers its own lenth as well as lenth of platform, Therefore total length becomes = 180+180 = 360m.

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Time taken is 18 seconds.

Therefore, required speed is

360/18= 20m/sec

Therefore, the correct answer is option E.

670. What should come in place of question mark (?) : 13 30 66 140 ? 592

A. 210

B. 290

C. 428

D. 430

E. None of these

Explanation :

13×2+4=30

30×2+6=66

66×2+8=140

290×2+12=592

Hence, the question mark should be replaced by 290

671. 8 men alone can complete a piece of work in 12 days. 4 women alone can complete the same piece of work in 48 days and 10 children alone can complete the piece of work in 24 days. In how many days can 10 men, 4 women and 10 children together complete the piece of work (in days)?

A. 5

B. 15

C. 28

D. 6

E. None of these

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Explanation :

From the given information we get:

Work done by (8×12) men = (4×48) women = (10×24) children i.e. work done by 1 man = 2 women = 2.5 children.

Now, the required time to finish to work:

M1D1H1/W1 = M2D2H2/W2

(10×24)/((10×2.5)+4×(2.5/2)+10)

= 6 days

672. Subhash starts a business by investing Rs 25000. 6 months later Aditya joins him by investing Rs 15,000. After another 6 months Aditya invests an additional amount of Rs 15,000. At the end of 3 years they earn a profit of Rs 2,47,000. What is Aditya's share in the profit?

A. Rs 1,30,000

B. Rs 1,23,000

C. Rs 1,05,000

D. Rs 1,11,500

E. None of these

Explanation :

Since it is a compound partnership , Therefore profit is divided in the ratio of I1T1 : I2T2

Where I is investment and T is time.

Subhash = 25000×36 = 900000/-

Thus, ration of the profits of Subash and Aditya will be 900000:810000 i.e.. 10:9

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Aditya's share = 9/(10+9) X 247000 = Rs. 117000

673. Ram’s age was square of a number last year and it will be cube of a number next year. How long must he wait before his age is again the cube of a number?

A. 39 years

B. 38 years

C. 10 years

D. 64 years

E. None of these

Explanation :

By a little guess work we can easily determine that the present age is 26 as next year it will be 27 which is the cube of 3. One year ago it was 25 ,

which is square of 5. Next cube will be at 64 so he has to wait for 38 years. Hence option B is the answer.

674. ‘A’ and ‘B’ can do a piece of work in 24 days and 32 days respectively. They started working together, After how many days should B leave so that the work is finished in 18 days.

A. 8 days

B. 4 days

C. 6 days

D. 2 days

E. None of these

Explanation :

Let total work is 96 units.

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So, A does 4 units per day.

B does 3 units per day.

As per the question, A remains for the whole time i.e. 18 days ,so out of 96 units he does 18x4=72 units.

So remaining 96 - 72 = 24 are done by B.

So B should leave after 24/3 = 8 days.

675. The difference between 38% of a number and 24% of the same number is 135.10. What is 40% of that number?

A. 394

B. 370

C. 378

D. 386

E. 390

Explanation :

Let the number be x,

Therefore, 0.38x – 0.24x = 135.10

We get x = 965

Thus, 0.40 × 965 = 386

676. The cost of 13 kg of sugar is Rs. 195/-. The cost of 17 kg. of rice is Rs. 544/- and the cost of 21 kg. of wheat is Rs. 336/-. What is the total cost of 21 kg of sugar, 26 kg of rice and 19 kg of wheat?

A. Rs. 1,451/-

B. Rs. 1,306/-

C. Rs. 1,500/-

D. Rs. 1,636/-

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E. None of these

Explanation :

Let the number be x,

13 kg sugar costs 195. So 1 kg costs 15.

17 kg rice costs 544, so 1 kg costs 32.

21 kg wheat costs 336, so 1 kg costs 16.

Hence 21 kg sugar + 26 kg rice + 19 kg wheat = (21 × 15) + (26 × 32) + (19 × 16) = 315 + 832 + 304 = Rs. 1451/-.

677. In an examination it is required to get 296 of the total maximum aggregate marks to pass. A student gets 259 marks and is declared failed. The difference of marks obtained by the student and that required to pass is 5%. What are the maximum aggregate marks a student can get?

A. 680

B. 780

C. 740

D. 749

E. None of these

Explanation :

Let the aggregate marks be x.

Therefore, 296 - 259 = 37 will be 5% of the x.

Thus (5/100) of x = 37 => x = 740.

DIRECTIONS for the questions 678 to 682 : Study the given information carefully to answer the given question:

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678. A boat takes a total time of twelve hours to travel 105 kms upstream and the same distance downstream. The speed of the boat in still water is six times of the speed of the current. What is the speed of the boat in still water? (In km/hr)

A. 12

B. 30

C. 18

D. 24

E. 36

Explanation :

Let ‘x’ be the speed of Boat in still water, and ‘y’ be the speed of current.

Then, according to the question,

Speed of the boat in still water = 6 speed of current

x = 6y

Also given that ,

105/(x+y) +105/(x-y) =12

105/7y +105/5y =12

12y=36

y=3

Therefore, x= 6×3=18

Speed of the boat in still water= 18kmph

679. The respective ratio between numbers of bags available in store P in August and that available in the same storein July was 5: 4. How many bags were available in store P in August as compared to July?

A. 150

B. 90

C. 24

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D. 60

E. 45

Explanation :

Number of bags available in P store in July = 20% of 600 = 120.

Now, since we have

Number of bags available in store P in August : Number of bags available in P store in July = 5:4

=> P : 120 = 5 : 4

Thus, number of bags available in Store P (In August) = (5/4)x120 = 150

680. In September, the total number of bags available in all the stores together was 90 more than that available in July, What was the percent increase in the total number of bags available in all the stores together from July to September?

A. 10

B. 12

C. 20

D. 18

E. 15

Explanation :

According to the question, Total number of bags available in September = 600+90= 690

% change =690-600/600 ×100=90/6 = 15

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681. In July, 4/15 of the available bags in store Q remained unsold and 5/12 of the available bags in store S remain unsold. How many bags were sold by stores Q and S together in July?

A. 159

B. 146

C. 154

D. 168

E. 163

Explanation :

Bags sold by store Q = (1- 4/15) of 25% of 600 = 11/15 of 25% of 600 = 110

And bags sold by store S = (1- 5/12) of 14% of 600 = 7/12 of 14% of 600 = 49

Thus, total bags sold by stores Q and S together in July = 159

682. Two years ago, the respective ratio between A's age at that time and B's age at that time was 5:9. A's age three years ago was 13 years less than B's age six years ago. What is B's present age?

A. 38 years

B. 30 years

C. 34 years

D. 32 years

E. 36 years

Explanation :

Two year ago, ratio between A’s age and B’s age at that time = 5:9

It means A’s age at that time = 5X, B’s age at that time = 9X

A’s age 3 year ago = 5X - 1, B’s age 6 years ago = 9X - 4

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As given in question, 9X – 4 – (5X - 1) = 13

Solving, we get X = 4

Thus, B’s Present age = 9X+2 = 9×4+2 = 38 years

683. A box contains 2 white, 3 black and 4 red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

A. 64

B. 32

C. 48

D. 96

E. None of these

Explanation :

Reqd. number of ways =( Total of 3 from 9)-( Total of 3 from 6 non black)=9C3–6C3 = 84 – 20 = 64

684. There are 3 vacancies in a firm and 15 applicants. Find the total number of ways of filling these vacancies.

A. 3375

B. 2730

C. 560

D. 600

E. None of these

Explanation :

Reqd. number of ways = 15 × 14 × 13 = 2730

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685. There is a natural number which becomes equal to the square of a natural number when 100 is added to it, and to the square of another natural number when 168 is added to it. Find the number.

A. 189

B. 69

C. 156

D. 224

E. None of these

Explanation :

Try by options. 3rd option is correct because 100 + 156 = 256 (square of 16) and 168 + 156 =

324 (square of 18).

No other option is satisfying the 2nd condition.

686. In a rectangular auditorium, chairs are arranged in rows and columns. The number of chairs in each column is more than the number of chairs in each row by 5. If there are in all 300 chairs, find the number of chairs in each row and in each column.

A. 25,20

B. 30,10

C. 23,18

D. None of these

Explanation :

Go by options. When there were 300 chairs, so product of chairs in rows and chairs in columns

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should be 300.

Difference of 5 should be there between the seats in rows and columns.

So no option out of 1st 3

is satisfying the conditions. So answer is 4th option and correct values are 20 and 15.

687. 629 ÷ 9.02 – 139.996 ÷ 7.06=?

A. 75

B. 35

C. 50

D. 65

E. 25

Explanation :

630 ÷ 9 – 140 ÷ 7

= 70 – 20 = 50

688. On a particular day, sweets were to be equally distributed among 960 students of a school. However, on that particular day 360 students remained absent, Hence each student present on that day got three sweets extra. Had all 960 students remained present that day, how many sweets would each, student have got?

A. 3

B. 5

C. 7

D. 8

Explanation :

Let number of sweets per student = X

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According to the given conditions, we have

960X = 600(X+3)

X = 5

So, the correct answer is option B.

689. What should come in place of the question mark (?) in the following number series ?

9 10 24 81 340?

A. 1376

B. 1780

C. 1570

D. 1725

E. None of these

Explanation :

Here, the pattern follows

9 × 1 + 1 =10

10 × 2 + 4 =24

24 × 3 +9 = 81

81 × 4 + 16 = 340

Similarly, 340 × 5 +25 = 1725

So, the correct answer is option D.

690. What would be the compound interest accrued on an amount of Rs9,000/- at the rate of 11 p.c.p.a. in two years ?

A. Rs.2088.90

B. Rs.2140.90

C. Rs.2068.50

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D. Rs. 2085

E. None of these

Explanation :

CI = A-P

CI = 9000 x(1+11/100)2- 9000=2088.90

So, the correct answer is option A.

691. What is the least number to be added to 2530 to make it a perfect square ?

A. 50

B. 65

C. 75

D. 80

E. None of these

Explanation :

Check for squares of the numbers which gives value around 2530, So

Square of 50 = 2500

Square of 51 = 2601

2601 - 2530 = 71 should be added.

So, the correct answer is option E(none of these).

692. The difference between 20% of a number and 45% of the same number is 125. What is 40% of that number ?

A. 186

B. 200

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C. 196

D. 465

E. None of these

Explanation :

Let no. be x, then

45% of x – 20% of x =125

So, x = 500

Therefore, 40% of 500 = 200

The correct answer is option B.

693. A train running at the speed of 108 kmph, crosses a 365 meter long platform in 21 secs. What is the length of the train?

A. 260 meters

B. 275 meters

C. 265 meters

D. 285 meters

E. None of these

Explanation :

Let the length of train = X meters

Speed of train = 108kmph = 108 × 5/18 = 30m/s

Distance = Speed × time

365 + X = 30 × 21

X = 265

So, the correct answer is option C.

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694. In order to pass in an examination, a student is required to get 280 marks out of the aggregate marks. Hema got 264 marks and was declared fail by 2 percent. What is the minimum passing percentage of the examination ?

A. 33%

B. 35%

C. 40%

D. 44%

E. None of these

Explanation :

Let maximum marks = X

Then, 2% of X = 280 - 264 = 16

=> X = 800

Then minimum passing %age = (280 /800) × 100 = 35

Therefore, the correct answer is option B.

695. he cost of 8 fans and 14 Ovens is Rs 36,520/-.What is the cost of 12 fans and 21 Ovens?

A. Rs. 56,800/-

B. Rs. 54,780/-

C. Rs. 57,950/-

D. Can't be determined

E. None of these

Explanation :

Let the cost of one fan be Rs.F and the Cost of Oven be Rs.O.

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Then, According to the question,

8F+14O = 36520

Dividing by 2, we get, 4F + 7O = 18260

Multiply by 3, we will get, 12F + 21O = 54780.

So, the correct answer is option B

696. Radius of a circular garden is 7 meter more than length of a rectangle whose perimeter is 364 meter and breadth is 84 meter. What will be cost of fencing the garden (only at the circumference), if the cost of fencing is Rs 8 per meter?

A. Rs. 5,456/-

B. Rs. 6,144/-

C. Rs. 5,296/-

D. Rs. 5,280/-

E. None of these

Explanation :

If the Length of rectangle = L meters

Then, according to the question,

2(L +84) = 364

=> L = 98

Radius of circle = 98 + 7 = 105 meters

Circumference of the circle = 2πr = 660

Cost of fencing = 660 × 8 = Rs 5280

Hence, the correct answer is option D.

697. If 43x + 43y = 4816, what is the average of x and y ?

A. 56

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B. 112

C. 62

D. 124

E. None of these

Explanation :

Divide the given equation by 43, we get, x + y = 112

Average = (x + y)/2 = 112/2 = 56

Hence, the correct answer is option A

698. A cricketer played 80 innings and scored an average of 99 runs. His score in the last inning was zero run. To have an average of 100 at the end, his score in the last innings should have been

A. 60 runs

B. 80 runs

C. 10 runs

D. 1 run

Explanation :

Let x be the score in the last inning to make the average of 100

Therefore, when average is 99, total score of 80 innings = 80 × 99 = 7920

And when the average is 100, total score of 80 innings = 80 × 100 = 8000

Therefore, x = 8000 – 7920 = 80

699. A man spends an average of Rs. 1,694.70 per month for the first 7 months and Rs.1,810.50 per month for the next 5 months. His monthly salary if he saves Rs. 3,084.60 during the whole year is

A. Rs. 1000

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B. Rs. 2000

C. Rs. 2400

D. Rs. 3000

Explanation :

Monthly Salary = [(1694.70*7)+(1810.5*5)+3084.60] / 12 = 24000/12 = 2000/-

700. A and B undertake to do a piece of work for Rs. 2,200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days. Find C's share.

A. Rs. 150

B. Rs. 275

C. Rs. 245

D. Rs. 175

Explanation :

Let 1 be the total work

Therefore, C’s one day work = [1/3]-[1/8 + 1/6]= 1/24

Ratio of share of A, B and C

i.e. A:B:C = 1/8 : 1/6 :1/24 => 3 : 4 : 1

So, C’s share = 1/8*2200=275

701. By selling an article at 80% of its marked price, a trader makes a loss of 10%. What will be the profit percentage if he sells it at 95% of its marked price?

A. 5.9

B. 12.5

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C. 6.9

D. 5

Explanation :

Let us assume the MP to be 900/-

Therefore, SP = 80% of MP = 0.80 × 900 = 720/-

As loss is 10%, so CP = 720/90 * 100=800

Now, if SP = 95% of MP = 0.95 × 900 = 855/-

Profit% = [{855-800}/800 ]*100 =6.87

702. By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% of the marked price. His gain during the sale season is

A. 8

B. 9

C. 7

D. 7.5

Explanation :

Given that SP of umbrella = 30/- and profit% = 20.

Therefore, CP of umbrella = 30/120 *100=25

SP of umbrella after 10% discount = 90/100 *30= 27

Thus, profit% = {(27-25) /25 }*100=8

703. The Arithmetic mean of 5, 10, 12, 18, 20 is:

A. 5

B. 65

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C. 13

D. 12

Explanation :

Arithmetic mean= 5+10+12+18+20/5=65/5=13

704. From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?

A. 4:1

B. 4:5

C. 5:2

D. 1:4

Explanation :

Let x and y be the two numbers, with x > y

Now are given that x -y/2=4[y - y/2]

Solving the above equation, we get x/y = 5:2

705. What is the remainder if 281 is divided by 5?

A. 4

B. 1

C. 2

D. 3

Explanation :

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706. What is the largest number which divides 150, 180 and 144 leaving the same remainder in each case?

A. 12

B. 3

C. 6

D. 8

Explanation :

HCF (180-150,180-144,150-144)

HCF(30,36,6)=6

707. In an examination, 52% of the candidates failed in English and 43% failed in Mathematics. If 17% failed in both the subjects, then the percentage of candidates, who passed in both the subjects, was

A. 25

B. 22

C. 23

D. 21

Explanation :

% of students failed in Mathematics only = 43% – 17% = 26%

% of students failed in English only = 52% – 17% = 35%.

So % of students passed in both = 100 – (26 + 35 + 17)

= 100 – 78 = 22%

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Alternate Solution:

% of students failed in Mathematics or English or both = 52% + 43% – 17% = 78%

So % of students passed in both = 100% – 78% = 22%. Hence, option B is correct.

708. What would be the compound interest drawn on an amount of Rs 18,400 @ 12 p.c.p.a. at the end of 3 years?

A. Rs. 4680.96

B. Rs. 7450.6752

C. Rs. 6235.2143

D. Rs. 8042.16

D. None of these

Explanation :

The formula for compound interest is:

CI = P(1+R/100)t - P

The required interest :

= 18400×[ (112/100)×(112/100)×(112/100) ] - 18400

= Rs. 7450.6752

709. What should come in place of question mark (?) : 3, 5, 15, ?, 1125, 84375,

A. 75

B. 20

C. 45

D. 80

E. None of these

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Explanation :

3 × 5 = 15

5 × 15 = 75

15 × 75 = 112

75 × 1125 = 84375

710. If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 27. If the sum of the two digits of the number is 11, what is the original number?

A. 47

B. 38

C. 74

D. Can't be determined

E. None of these

Explanation :

Let the original number be 10x + y

New number = 10y + x

Now, 10y + x - (10x + y) = 27

=> 9y - 9x = 27

We have, different of the two digits = 27 / 9 = 3

Sum of the two digits is = 11

Now, the two digits are (11+3 / 4) and (11-3 / 2) i.e. 7 and 4

Thus, the number is 47 because 47 < 74.

You can check it: 74 - 47 = 27

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711. 59.99% of 255.012 + 22.98% of 182.005 = ?

A. 162

B. 146

C. 195

D. 225

E. 178

Explanation :

59.99% of 255.012 + 22.98% of 182.005 can be written as :

~= 60% of 255 + 23% of 182

~= 153 + 41.86

~= 194.86

712. 12 × 958 ÷ 17 = ?

A. 532

B. 675

C. 765

D. 483

E. 806

Explanation :

12 × 958 ÷ 17 = 676

713. Wages for 40 women amount to Rs. 15000 in 60 days. How many men must work for 15 days to receive Rs. 6000? The daily wage of a man is double that of a woman.

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A. 28 men

B. 30 men

C. 32 men

D. 35 men

E. None of these

Explanation :

Daily wage of woman = 15000 / (60*40) = 6.25

Therefore, daily wageof man = 2 × 6.25 = 12.5

Number of men = 6000 / (15×12.5) = 32

714. The simple interest on a certain sum of money for 2 years at 8% p.a. is Rs. 600. What is the compound interest at the same rate and for the same time?

A. Rs. 620

B. Rs. 624

C. Rs. 625

D. Rs. 630

E. None of these

Explanation :

SI for 1 year will be 600 / 2 = Rs.300.

As in 1st year SI and CI are same.

So 1st year CI will also be Rs.300.

In CI, in second year 300 will also be added in principal.

So second year CI = 300 + 8% of 300 = 324.

So total CI after 2 years = 300 + 324 = Rs. 624.

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715. The cost of 13 kg of sugar is Rs. 195/-. The cost of 17 kg. of rice is Rs. 544/- and the cost of 21 kg. of wheat is Rs. 336/-. What is the total cost of 21 kg of sugar, 26 kg of rice and 19 kg of wheat?

A. Rs. 1,451/-

B. Rs. 1,306/-

C. Rs. 1,500/-

D. Rs. 1,636/-

E. None of these

Explanation :

13 kg sugar costs 195. So 1 kg costs 15.

17 kg rice costs 544, so 1 kg costs 32.

21 kg wheat costs 336, so 1 kg costs 16.

Hence 21 kg sugar + 26 kg rice + 19 kg wheat = (21 × 15) + (26 × 32) + (19 × 16)

= 315 + 832 + 304 = Rs. 1451.

716. The difference between 38% of a number and 24% of the same number is 135.10. What is 40% of that number?

A. 394

B. 370

C. 378

D. 386

E. None of these

Explanation :

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Let the number be x

Therefore, 0.38x – 0.24x = 135.10

We get x = 965

Thus, 0.40 × 965 = 386

717. In an examination it is required to get 296 of the total maximum aggregate marks to pass. A student gets 259 marks and is declared failed. The difference of marks obtained by the student and that required to pass is 5%. What are the maximum aggregate marks a student can get?

A. 690

B. 780

C. 740

D. 749

E. None of these

Explanation :

Let the aggregate marks be x.

Therefore, 296 - 259 = 37 will be 5% of the x.

Thus (5 / 100) of x = 37 => x = 740.

718. When n is divided by 6, the remainder is 4. When 2n is divided by 6, the remainder is

A. 2

B. 0

C. 4

D. 1

Explanation :

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When n is divided by 6, the remainder is 4. Hence,the number can be written as n = 6k +4

hence, 2n = 12k + 8 and when 2n is divided by 6 : remainder will be ( 12 k + 8 ) / 6 = 2

So,12k gives remainder 0 with 6 and 8 gives remainder 2 with 6. So, remainder is 0 + 2 = 2.Hence, Ans is option A.

719. The value of is 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 is

A. 1/10

B. 3/5

C. 3/20

D. 7/20

Explanation :

1/(4×5) + 1/(5×6) + 1/(6×7) + 1/(7×8) + 1/(8×9) + 1/(9×10)

= (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8) + (1/8 - 1/9) + (1/9 - 1/10)

= 1/4 -1/10 = 3/20

720. Let a = 1/(2 - √3) + 1/(3 - √8) + 1/(4 - √15). Then we have

A. a > 18

B. a >= 18

C. a = 18

D. a = 9

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721. If part of a journey takes 10 minutes, then to complete ( 3 / 5 )th of that journey, it will take

A. 40 minutes

B. 45 minutes

C. 48 minutes

D. 36 minutes

Explanation :

part of journey means = 4 - 155/40 = 5/40th of the journey will take 10 mins

Hence, for the full journey it will take 80 mins

Therfore for 3/5 th of the journey,it will take = ( 3/5 ) * 80 = 48 mins

Hence, Ans is option C.

722. A reduction of 20% in the price of rice enables a customer to purchase 12.5 kg more for Rs. 800. The original price of rice per kg is

A. Rs. 14

B. Rs. 16/-

C. Rs. 12/-

D. Rs. 15/-

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Explanation :

Let the price of rice is Rs x / kg

As per the question

800/ 0.8x - 800 / x = 12.5

160/0.8x = 12.5

on solving x= 16

723. In two alloys A and B, the ratio of zinc to tin is 5 : 2 and 3 : 4 respectively. Seven kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy?

A. 2:1

B. 1:2

C. 2:3

D. 1:1

Explanation :

Alloy A : which weighted 7 kg has zinc & tin in ratio = 5 : 2 i.e Zinc in alloy A = 5 kg & tin in alloy A = 2kg

Alloy B : which weighted 21 kg has zinc & tin in ratio = 3 : 4 i.e Zinc in alloy A = 9 kg & tin in alloy A = 12kg

Hence, total Zinc : total tin = 14 : 14 = 1 : 1 So, answer is option D.

724. If A : B = 3 : 4 and B : C = 6 : 5, then C : A is

A. 10;9

B. 9:10

C. 8:9

D. 9:8

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Explanation :

A : B = 3 : 4 and B : C = 6 : 5,

Then C : A will be = A : B : C = 9 : 12 : 10

Hence, ratio of C : A = 10: 9.

DIRECTIONS for the questions 1 to 10: Solve the following question and mark the best possible option.

725. If a population of yeast cells grows from 10 to 320 in a period of five hours, what is the rate of growth?

A. It doubles its numbers every hour.

B. It triples its numbers every hour

C. It doubles its numbers every two hours.

D. It triples, its numbers every two hours

Explanation :

Cells grow from 10-320, so let the growth % be R per annum.

So it doubles itself in every hour.

726. The number of red blood corpuscles in one cubic millimeter is about 5,000,000, and the number of white blood corpuscles in one cubic millimeter is about 8,000. What, then, is the ratio of white blood corpuscles to red blood corpuscles?

A. 1:625

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B. 1:40

C. 4:10

D. 5:1250

Explanation :

8000 : 5,000,000 = 8 : 5000 =1:625.

727. Which of the following numbers can be divided evenly by 19?

A. 54

B. 63

C. 76

D. 82

Explanation :

76 comes in table of 19.

728. A rectangular tract of land measures 860 feet by 560 feet. Approximately how many acres is this? (one acre = 43,560 square feet)

A. 12.8 acres

B. 11.06 acres

C. 10.5 acres

D. 8.06 acres

Explanation :

Area of the rectangular tract = Length x Breadth = 860 x 560 Sq.ft. = {860x560}/43560 acres = 11.06 acres.

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729. On a particular morning the temperature went up 1 ° every two hours. If the temperature was 53° at 5 A.M., at what time was it 57°?

A. 7 a.m.

B. 8 a.m

C. 12 p.m

D. 1 p.m

Explanation :

Difference in temperature= {57-53}= 4 degrees. 1 degrees rise happens in 2 hours , so 4 degrees rise would happen in 4 x 2 = 8 hrs, so it will be 8 hrs after 5 A.M. i.e. 1 P.M.

730. For health reasons, Amir wants to drink eight glasses of water a day. He has already had six glasses. What fraction is Amir left with?

A. 1/8

B. 1/6

C. 1/4

D. 1/3

Explanation :

The fraction of water he drank = 6/8= ¾, so fraction left = 1-3/4 = 1/4.

731. A movie is scheduled for two hours. The theatre advertisements are 3.8 minutes long. There are two previews; one is 4.6 minutes long, and the other is.2.9 minutes long. The rest of time is devoted to the feature film. How long is the feature film?

A. 108.7 minutes

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B. 97.5 minutes

C. 118.98 minutes

D. 94.321 minutes

Explanation :

Total time apart from the feature film = { 3.8 + 4.6 + 2.9 }=11.3 minutes, therefore time for feature film = { 120-11.3}min= 108.7 min.

732. Twelve is 20% of what number?

A. 5

B. 20

C. 60

D. 240

Explanation :

20% of a no. is 12, so no.= 12/20%= 60.

733. The product of two and four more than three times a number is 20.What is the number?

A. 2

B. 16

C. 44

D. 87

Explanation :

The equation is 2 X {3x+4} = 20, x=2.

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734. Find three consecutive odd integers whose sum is 117.

A. 31, 33, 35

B. 37, 39, 41

C. 38, 39, 40

D. 39, 41, 43

Explanation :

Let the three integers be 2x + 1, 2x + 3 , 2x + 5. Therefore, 6x + 9 = 117, x = 18 The three integers are 37, 39, 41.

735. The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age?

A. 30 years

B. 38 years

C. 40 years

D. 42 years

E. None of these

Explanation :

Total sum of man's age & his son's age =28 Ã— 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man's age = (3/4) Ã— 56 = 42 So, the correct answer is option D.

So, the correct answer is option D.

736. A basket contains 3 blue, 5 black and 3 red balls. If 3 balls are drawn at random what is the probability that all are black?

A. 2/11

B. 1/11

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C. 3/11

D. 8/33

E. None of these

Explanation :

Ways of selecting 3 black balls out of 5 - 5C3 Total ways of selecting 3 balls - 11C3 The required probability = (5C3 / 11C3 ) = (10/165) = (2/33)

737. The ratio of the capacity to do work of A and B is 3 : 2. If they together can complete a work in 18 days, then how long does A take to complete the work alone?

A. 45

B. 30

C. 24

D. 40

E. None of these

Explanation :

Let A and B take 3x and 2x days to complete the work

1/3x+1/2x=1/18 ;x=15

So A will take 45 days.

738. How many integers are there between 300 and 600 that are divisible by 9?

A. 33

B. 31

C. 28

D. 25

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E. None of these

Explanation :

The sequence is 306,â€¦ 594 594=306+(n-1)9â‡’288=(n-1)9â‡’n=33

739. The sum of two numbers is 14. If the sum of their reciprocals is 7/24, find the numbers:

A. 4,8

B. 8,12

C. 4,10

D. 6,8

E. None of these

Explanation :

Going by option , option number 3 and 4 will give sum = 14 but 4th option will give l.c.m 24 and third option gives LCM as 20. It has to be the fourth option.

740. A, B, C and D are four consecutive odd numbers and their average is 42. What is the product of B and D?

A. 1860

B. 1890

C. 1845

D. 1677

E. None of these

Explanation :

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As there are As diff. Is same so average should lie between B and C so B is 41 & C is 43 so D must be 45 as we have to find the product of B and D so it would be 1845.

741. The product of two alternative multiples of 4 is eight more than five times their sum. What are the two numbers?

A. 16,32

B. 12,20

C. 8,16

D. 16,24

E. None of these

Explanation :

Though options, 3rd option satisfies all the conditions.

742. Find the three terms in arithmetic series such that their sum is 30 and product is 910

A. 8,10,12

B. 7,10,13

C. 6,10,14

D. 5,13,14

E. None of these

Explanation :

Option 2nd gives product 910.

743. A car covers the first 30 km of its journey in 45 minutes and the remaining 25 km in 30 minutes. What is the average speed of the car?

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A. 40km/hr

B. 64km/hr

C. 49km/hr

D. 48km/hr

E. None of these

Explanation :

Average speed = = 44 km/hr So option E is the answer.

744. What is 25% of 30% of 2/5 of 2000 ?:

A. 36

B. 40

C. 56

D. 60

E. none of these

Explanation :

25% of 30% of 2/5 of 2000 1/4 A— 3/10 A— 2/5 A— 2000 =60

DIRECTIONS for the questions 1 to 5: Solve the following question and mark the best possible option.

745. A boat takes a total time of twelve hours to travel 105 kms upstream and the same distance downstream. The speed of the boat in still water is six times

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of the speed of the current. What is the speed of the boat in still water? (In km/hr)?

A. 12

B. 30

C. 18

D. 24

E. 36

Explanation :

Let ‘x’ be the speed of Boat in still water, and ‘y’ be the speed of current.

Then, according to the question,

Speed of the boat in still water = 6 speed of current

x = 6y

Also given that ,

105/(x+y) +105/(x-y) =12

105/7y +105/5y =12

12y=36

y=3

Therefore, x= 6×3=18

Speed of the boat in still water= 18kmph

746. At 60% of its usual speed, a train of length L metres crosses platform 240 metres long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in metres)?

A. 440

B. 425

C. 220

D. 480

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E. 240

Explanation :

Let usual speed = S m/s.

According to the question,

60% of S= (L+240)/15

9S= L+240………… (i)

Also given that, S = L/6

L = 6S …. (ii)

From (i) & (ii)

9S= 6S+240

3S= 240

S=80 m/s

From (ii)

L= 6×80 =480 m

747. P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of what Q has. If P, Q and R together have Rs. 240 then how much money does P alone have? (in Rs.)

A. 75

B. 60

C. 120

D. 80

E. 90

Explanation :

Assume that P has 2x amount

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Therefore, Q = 3x amount (50% more than P)

And R = 3x × 1/3 = x

Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1

Thus, P alone have = (2/6) × 240 = Rs. 80

748. A and B both start a small business with an investment of Rs. 3500 and Rs. 5600 respectively. At the end of few months from the start of the business, A withdrew from the business completely. If the annual profit was divided between A and B in the respective ratio of 5 : 12, then after how many months from the start of the business, did A leave the business?

A. Eight

B. Nine

C. Ten

D. Five

E. Four

Explanation :

Let A invested his money for ‘X’ months.

A : B

3500×X : 5600×12 35X : 672

As A and B have profit ratio as 5:12

Thus,35x/672 =5/12

X=8

Hence, A has invested money for 8 months

749. The difference between S.I and C.I on certain of money for 3 years at 10% per annum is Rs. 248. Find the sum?

A. 2000

B. 8000

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C. 1600

D. 4000

E. None of these

Explanation :

Let us consider sum of money is Rs. 1000.

S.I. = 1000*10*3/100 =300

C.I. = 1000(1+10/100)*(1+10/100)*(1+10/100)-1000 =331

Difference between SI and CI = 331 – 300 = 31

Rs. 31 is difference, when sum = Rs. 1000

Rs. 248 is Difference, then sum = 1000*248/31 =8000.

DIRECTIONS for the questions 6 to 8: Solve the following question and mark the best possible option.

X ≤ Y

X ≥ Y

X > Y

X < Y

X = Y or No relationship between X and Y

750.

i. 2x2 + 7x + 5 = 0

ii. 3y2 + 5y + 2 = 0

Explanation :

I. 2x2 +7x+5 = 0

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=> x = - 5/2, -1

II. 3y2+5y+2=0

=> y = -3/2, -1

Thus, X ≤ Y

751.

i. 2x2 -13x + 21 = 0

ii. 3y2 -14y + 15 = 0

Explanation :

I. 2x2 -13x+21=0

=> x = 3, 7/2

II. 3y2-14y+15=0

=> y = 3, 5/3

Hence, X ≥ Y

752.

i. 2x2 - 13x + 18 = 0

ii. y2 – 7y + 12 = 0

Explanation :

I. 2x2 -13x+18=0

=> x = 9/2, 2

II. y2-7y+12=0

=> y = 4,3

Thus, no relationship between X and Y

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753. A can do a piece of work in 20 days. He worked for 5days. After this B did the remaining work in 3 days. How many days A and B will together take to finish the whole work?

A. 10 days

B. 10/3 days

C. 5/3 days

D. 12 days

E. None of these

Explanation :

A’s one day work = 1/20 ; A’s = five day work = 5/20 = 1/4 , Remaining work = 1- 1/4 =3/4 , B can do 3/4 of work in 3 days, B can do 1 work in 3*4/3=4 days, B’s one day work = 1/4 , A’s one day work = 1/20, (A+B)’s one day work 1/4 +1/20 = 5+1/20 = 6/20 =3/10 . So, A and B together can do the work in 10/3 days.

754. A and B can do a piece of work in 10 days, B and C in 12 days and C and A in 15 days. If B alone works for 15 days and then joined by A and C, in how many days will the work be finished?

A. 20 days

B. 15 days

C. 16 days

D. 18 days

E. 12 days

Explanation :

A + B)’s one day work = 1/10; (B + C)’s one day work =1/12 ;

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(C+A)’s one day work = 1/15 . 2(A + B + C)’s one day work = 1/10 + 1/12 +1/15 = 6+5+4/60 = 15/60 = 1/4 ;

A + B + C one day work =1/8 ; B’s 1 day work = (A + B + C)’s 1 days work – (C + A)’s 1day work = 1/8 -1/15 7= 15-8/120 = 7/120; B’s 15 day work = 7/120 *15 = 7/8 Remaining work = 1-7/8 = 1/8.

This remaining is to be done by A + B + C , A + B + C does 1 work in 8 days. A + B + C does 1/8 of work in 8 *1/8 = 1 day.

Total time taken to finish the work = 15 + 1 = 16 days.

755. A is able to do a piece of work in 15 days and B can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

A. 8/15

B. 7/15

C. 11/15

D. 2/11

E. Other than those given as options

Explanation :

Total work done by A + B in 1 day = 1/15 + 1/(20 ) = 7/60

Work done in 4 days = 7/60 × 4 = 7/15

Therefore, fraction of work left = 1 - 7/15 = 8/15

756. Cost price of each of the articles A and B is Rs. 'X'. Article A was sold at a profit of 10% and article B was sold at a profit of 30%. If the overall profit earned after selling both the articles is Rs. 136/-, what is the value of 'X'?

A. Rs.340/-

B. Rs.300/-

C. Rs.360/-

D. Rs.380/-

E. Rs.320/-

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Explanation :

Given : 0.1x + 0.3x = 136 => x = 340

757. Population of a village increased by 5% from 2007 to 2008 and by 25% from 2005 to 2009. If the population of the village was 480 in 2007, what was its population in 2009?

A. 640

B. 610

C. 630

D. 620

E. 650

Explanation :

Population in 2007 = 480

In 2008 = 1.05 × 480 = 504

In 2009 = 1.25 × 504 = 630

758. 24% of 150 × 3/4= ?

A. 64

B. 40

C. 72

D. 24

E. 48

Explanation :

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24% of 150 × 3/4= x = 36 × 4/3 = 48

759. In the month of March, Hiten spent 45% of his monthly salary on paying bill and rent. Out of the remaining salary, he invested 60% in PPF and the remaining he deposited in bank. He deposited Rs. 15,400 in bank. If in April, he got an increment of 10%, what was his salary in April?

A. Rs. 84,000

B. Rs. 77,000

C. Rs. 1,10,000

D. Rs. 59,000

E. Rs. 68,000

Explanation :

Let the initial salary of Hiten be ‘S’. Then:

(0.55 × 0.4) S = 15400 => S = 70000

After increment, Hiten’s salary = 1.1 × 70000 = 77000

760. A person covers a certain distance by travelling at a uniform speed of 120 km/h for 90 minutes. At what speed will he have to travel in order to cover the same distance in 1 hour 20 minutes? (in km/h)

A. 135

B. 125

C. 140

D. 130

E. 145

Explanation :

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Distance = 120 × 90/60 = 180 km Speed required to cover 180 km in 1 hr 20 mins ( 4/3 hrs) = 180 × ¾ = 135 km/hr

761. In Jar A, 120 litres milk was mixed with 24 litre water. 12 litre of this mixture was taken out and 3 litre water was added. If 27 litre of newly formed mixture is taken out, what will be the resultant quantity of water in the jar? (In litre)

A. 20

B. 10

C. 15

D. 30

E. 25

Explanation :

Ratio of milk : water in Jar A = 120 : 24 = 5 : 1

12 lts of this mixture is taken out => milk = 5/6 × 12 = 10 lts and water = 2 lts taken out

3 lts of water added = 24 – 2 + 3 = 25 lts => new ratio of milk : water

= 110 : 25 = 22 : 5

Now 27 lts of this mixture is again taken out =>

water taken out = 5/27 × 27 = 5 lts

water left = 25 – 5 = 20 lts

762. A boat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream? (in km/hr)

A. 10

B. 6

C. 5

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D. 4

E. 15

Explanation :

Speed of boat = 15 k/h

Let the speed of stream be ‘S’

Given : 30/(15+S) + 30/(15-S) = 9/2

Solving we get, S = 5 km/h

763. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's present age?

A. 16 years

B. 18 years

C. 20 years

D. 22 years

E. 25 years

Explanation :

Let the ages of Kunal and Sagar be K and S respectively.

Given : (K-6)/(S-6) = 6/5 => 5K – 6S = -6 ……(i)

And: (K+4)/(S+4) = 11/10 => 10K – 11 S = 4 …..(ii)

Solving (i) & (ii) we get: S = 16 years.

764. In an election there were only two candidates. One of the candidates secured 40% of votes and is defeated by the other candidate by 298 votes. The total number of votes polled is

A. 1490

B. 1500

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C. 745

D. 1460

Explanation :

Let x be the total no of votes

Therefore, 40% × x + 298 = 60% × x => 20% × x = 298 => x = 1490

Alternatively we can also say if one candidate got 40 % votes then other got 60 % votes , Therefore difference is 20 % votes

20 % of votes = 298

Therefore 100 % = 1490.

765. If |2x + 3| > 8, then which of the following is true?

A. -5.5 > x > 2.5

B. 2.5 > x > -5.5

C. 5.5 > x > -2.5

D. -5.5 > x > -2.5

Explanation :

Either ( 2x + 3 ) > 8 or –( 2x + 3 ) > 8, so we get 2x > 5 or -2x > 11 i.e. x > 2.5 or x < -5.5 - 5.5 > x > 2.5

766. In a container there is 90 ltrs of mixture of milk and water in the ratio 11:4. What part of the mixture should be replaced with same quantity of water, so that the ratio after replacement becomes 11:7?

A. 5/6

B. 3/11

C. 1/6

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D. 1/3

Explanation :

In 90 ltrs., the ratio of milk and water is 11:4 i.e. M = 66 ltr & W = 24 ltr

After the replacement, the ratio becomes 11:7, i.e. M = 55 ltr & W = 35 ltr

Since qty. of milk is reduced to1/6th , therefore the overall removal is also 1/6th

767. Ram can do a certain work in 16 days and Shyam can do the same work in 10 days. If they start the work together, then how many days early can Shyam quit, if the work is to be done in 8 days?

A. 3 days

B. 5 days

C. 6 days

D. 2 days

Explanation :

Ram does (1/16) × 8 = 1/2 work in 8 days, so the other half has to be done by Shyam, for which he will need 10/2 = 5 days. So he can quit ( 8 - 5 ) = 3 days early.

768. A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?

A. 25

B. 30

C. 35

D. 40

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Explanation :

Let 'x' red marbles will be added to the jar Then, according to the conditions,

( 10 + x ) = 60 / 100 × ( 40 + x ) ==> x = 35

769. If a number multiplied by 25% of itself gives a number which is 200% more than the number, then the number is

A. 12

B. 16

C. 20

D. 24

Explanation :

Let the no. be x.

Then x * ( 25/100 * x ) = x + 200/100 * x

==> x = 12

770. The square root of ( 7 + √35 ) ( 7 - √35 ) is

A. √14

B. √17

C. 14

D. 3√5

771. If √5 = 2.236, then the value of ( √5 / 2 ) - ( 10 / √5 ) + √125 is equal to

A. 5.59

B. 7.826

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C. 8.944

D. 10.062

Explanation :

772. A number X is 150 more than a second number, Y. If the sum of X and Y is 5 times Y, what is the value of Y ?

A. 50

B. 40

C. 80

D. 60

E. 70

Explanation :

X = 150 + Y

X + Y = 5Y

150 + 2Y = 5Y

150 = 3Y => Y = 50

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773. A square field has an area of 50625 m2. Find the cost of fencing around it at Rs. 15 per metre, (in Rs.)

A. 12,500

B. 6750

C. 17,500

D. 13500

E. 16250

Explanation :

Area of square field = 50625 => side of the field = = 225

cost of fencing @ Rs. 15/ meter = 4 × 225 × 15 = Rs. 13500

774. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What will be the weight of the new person ?

A. 76

B. 76.5

C. 85

D. 80

E. 90

Explanation :

Increased wt. of 8 persons = 8 × 2.5 = 20 kg

=>wt. of new person = 65 + 20 = 85 kg

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775. 50% of a number is 18 less than two-third of that number. Find the number ?

A. 123

B. 115

C. 119

D. 108

E. 101

Explanation :

Let the no. be x

Given : 50x/100 = 2x/3 – 18

½ x – 2/3 x = - 18

=> x = 108

776. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648

B. 1800

C. 2700

D. 2000

E. 3080

Explanation :

Let the no. of bottles be ‘B’. Using chain rule:

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777. 652.84 + 482.26 + ? = 1200

A. 62.16

B. 54.18

C. 56.1

D. 64.9

E. 66.1

Explanation :

652.84 + 482.26 + x = 1200,=> 1135.1 + x = 1200 => x = 64.9

778. 60% of 250 -? = 75

A. 25

B. 45

C. 60

D. 75

E. 100

Explanation :

=>60% of 250 - x = 75

= 150 – x = 75 => x = 75

779. 681 + ? * 40 = 1161

A. 14

B. 12

C. 24

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D. 16

E. 8

Explanation :

681 + x × 40 = 1161

= 681 + 40x = 1161 => 40x = 1161 – 681 = 480

=> x = 480/40 = 12

780. Different words are formed with the help of the letters of word RELATION. Find the number of ways in which vowels always occupy even places.

A. 292

B. 654

C. 356

D. 576

E. 8!

Explanation :

Vowels i.e. A, E, I, O can be arranged = 4C4 ×4! = 4! ways.

Remaining letters R, L, T, N can be arranged in = 4! ways. So the total number of ways = 4! ×4! = 576 ways.

781. The number of ways in which 8 persons can be seated at a round table if 2 particular persons must always sit together

A. 288

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B. 720

C. 1440

D. 2880

E. None of these

Explanation :

Reqd. number of ways = 2! × (7 – 1)! = 2! × 6! = 1440

782. Simple interest on Rs. 1200 @ 13 p.c.p.a. for 'X' years is Rs. 624/-. What is the amount on Rs. 'X+1000' at the same rate of interest for 3 years?

A. Rs. 1872/-

B. Rs. 1384/-

C. Rs. 936/-

D. Other than those given as options

E. Rs. 1404/-

Explanation :

624 = (1200×13×x)/100 => x = 4

Now, P = x + 1000 = 4 + 1000 = 1004

I = (1004×13×3)/100 = 392

=> amount = 1004 + 392 = 1396/-

783. A circle and rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What will be the area of the circle? (in cm2)

A. 88

B. 1250

C. 154

D. 128

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E. Other than those given as options

Explanation :

Perimeter of rectangle = perimeter of circle = 2 (18 + 26) = 88

2Πr = 88 => r = 14cm

Area of circle = 22/7 ×14 × 14 = 616 cm2

784. 101 + 1001 + 2003 + 30005 + 9056 =?

A. 42616

B. 42166

C. 41266

D. 42156

E. 42661

Explanation :

=>101 + 1001 + 2003 + 30005 + 9056 = 42166.

785. 5/6th of 348 -1/8th of 232 = ?

A. 267

B. 258

C. 257

D. 261

E. 263

Explanation :

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=>5/6th of 348 -1/8th of 232 = x

=> x = 290 – 29 = 261

786. 3060 -2460 = ? × 30

A. 30

B. 50

C. 20

D. 60

E. 43

Explanation :

=>3060 -2460 = x * 30

=> 600 = 30x => x = 20

787. The product of the digits of a two-digit number is twice as large as the sum of its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.

A. 36

B. 27

C. 63

D. 46

E. None of these

Explanation :

Go by options. 3rd option is the answer because 63 Þ product of digits = 6*3 = 18. Sum of digits = 6 + 3 = 9.

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Hence product of digits is twice as the sum of the digits. Also 63 – 27 = 36. So digits are reversed.

788. The product of the digits of a two-digit number is one-third of that number. If we add 18 to the required number we get a number consisting of the same digits written in reverse order. Find the number.

A. 42

B. 24

C. 72

D. 27

E. None of these

Explanation :

Go by options 2nd option correct because 24 = 3*2*4 . Number is thrice the product of its digits

24+18 = 42. Hense digits are reversed.

789. Jar A has 60 litres of mixture of milk and water in the respective ratio of 2: 1. Jar B which had 40 litres of mixture of milk and water was emptied into Jar A, as a result in Jar A, the respective ratio of milk and water becomes 13 : 7. What was the quantity of water in Jar B?

A. 8 litres

B. 15 litres

C. 22 litres

D. 7 litres

E. 1 litres

Explanation :

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Jar A has 60 Liters.

Radio between milk and water 2:1;

Quantityof milk in Jar A=2/3*60 = 40;

Quantityof waterin Jar A=1/3*60 = 20;

40 Liters of Mixture B having Milk and Water is empty;

Therefore ,total Mixture = 60 + 40 =100;

The respective Ratio of Milk and Water is 13:7;

Quantity of Milk in Jar A = 13 /20 *100 = 65;

Quantity of Waterin Jar A = 7/20 *100 = 35;

Quantity of Waterin Jar B = 35 -20 = 15 liters.

790. The sum of a series of 5 consecutive odd numbers is 195. The second lowest number of this series is one less than the second highest number of another series of 5 consecutive even numbers. What is 40% of the second lowest number of the series of consecutive even numbers?

A. 16.8

B. 14.8

C. 19.4

D. 17.6

E. 13.6

Explanation :

The sum of the series of 5 Consecutive odd numbers is 195;

Let the Series of Consecutive odd numbers is X, X+2, X+4, X+6, X+8 ;

X+X+2+X+4+X+6+X+8 = 195 ;

5X+20 = 195;

X=35.

Series of consecutive odd numbers is 35, 37 , 39 , 41 ,43 ;

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According to the question ,the second lowest number of this series is less than the ;

Second highest number of another series of 5 consecutive numbers;

Second lowest number is 37;

Second highest number of another series of 5 consecutive numbers = 37 +1 = 38 ;

Therefore , another series of 5 consecutive no 32 , 34 ,36 ,38 , 40 ;

40% of the lowest of the series of consecutive numbers = 34 *40 / 100 = 13.6.

791. The sum of the dimensions of a room (i.e. length, breadth and height) is 18 metres and its length, breadth and height are in the ratio of 3 : 2 : 1 respectively. If the room is to be painted at the rate of Rs. 15 per m2, what would be the total cost incurred on painting only the four walls of the room (in Rs.)?

A. 3250

B. 2445

C. 1350

D. 2210

E. 2940

Explanation :

Ratio of length : breadth : height = 3 : 2 : 1

Sum of dimensions of room = 18

Length = 3/6×18 = 9

Breath = 2/6×18 = 6

Height = 1/6×18 = 3

Area of four walls = 2h×(l+b) = 2×3(9+6) = 90

Total cost of painting four walls = 90×15 = 1350

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792. There are 3 vacancies in a firm and 15 applicants. Find the total number of ways of filling these vacancies

A. 3375

B. 2730

C. 560

D. 600

E. None of these

Explanation :

Reqd. number of ways = 15 × 14 × 13 = 2730

793. The number of ways of selecting four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is

A. 27378

B. 29465

C. 26368

D. 11448

E. None of these

Explanation :

Reqd. number of ways = 30C4 – 27= 27378. Here 27 are the number of ways in which we can have 4 consecutive numbers

794. A train does a journey without stopping in 8 hours. If it had traveled 5 km an hour faster, it would have done the journey in 6 hours 40 min. What is its slower speed?

A. 35 km/hr

B. 25 km/hr

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C. 40 km/hr

D. 20 km/hr

E. 30 km/hr

Explanation :

795. A person sets to cover a distance of 12 km in 45 minutes. If he covers 3/4 of the distance in 2/3 of time, then what is the speed in the remaining time?

A. 16 km/hr

B. 8 km/hr

C. 12 km/hr

D. 55 km/hr

E. 10 km/hr

Explanation :

796. If 8 men or 12 women can do a piece of work in 25days, in how many days, can the work be done by 6 men and 11 women working together?

A. 12 days

B. 15 days

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C. 9 days

D. 18 days

E. 10 days

Explanation :

797. Some men promised to do a job in 18 days, but 6 of them became absent and remaining men did the job in 20 days. What is the original number of men?

A. 50 men

B. 60 men

C. 65 men

D. 70 men

E. 55 men

Explanation :

Let the number of men originally = M. According to the given condition M * 18 = ( M – 6) * 20 =>M = 60

798. The product of the digits of a two-digit number is one-third of that number. If we add 18 to the required number we get a number consisting of the same digits written in reverse order. Find the number

A. 42

B. 24

C. 72

D. 27

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E. None of these

Explanation :

Go by options. 2nd option is correct because 24 = 3 *2 *4. Number is thrice the product of its digits.

Also 24 + 18 = 42. Hence digits are reversed.

799. Bill, Simon, and John are brothers, given Simon is the eldest. Bill is as many years younger than one brother as he is older than the other. Simon is 7 years younger than twice the age of John. John is 5 years older than half the age of Bill. What is the sum of the ages of Bill, Simon and John?

A. 12

B. 24

C. 48

D. 42

E. Can’t say

Explanation :

S - B = B - J; J = B/2 + 5;

S = 2J - 7; S = B + 10 - 7 = B-3;

J= B/2 + 5 ; 2S =B + 10;

B/2 + 5 + B + 3 = 2B;

B/2 = 8 ; B = 16 ; S = 19 ; J = 13;

So B - S - J =16 - 19 - 13 = 48;

800. Cost price of each of the articles A and B is Rs. 'X'. Article A was sold at a profit of 10% and article B was sold at a profit of 30%. If the overall profit earned after selling both the articles is Rs. 136/-, what is the value of 'X'?

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A. 2

B. 16

C. 44

D. 87

Explanation :

Given : 0.1x + 0.3x = 136 => x = 340

801. Population of a village increased by 5% from 2007 to 2008 and by 25% from 2005 to 2009. If the population of the village was 480 in 2007, what was its population in 2009?

A. 640

B. 610

C. 630

D. 620

E. 650

Explanation :

Population in 2007 = 480

In 2008 = 1.05 × 480 = 504

In 2009 = 1.25 × 504 = 630

802. The fourth root of 24010000 is

A. 7

B. 49

C. 490

D. 70

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Explanation :

√24010000 = 4900

Again, √4900 = 70

∴ 4√√24010000 = 70

803. The greatest 4 digit member which is a perfect square, is

A. 9999

B. 9909

C. 9801

D. 9081

Explanation :

The greatest four -digit perfect square will be the square of the greatest two digit number, hence it will be 99 × 99 = 9801.

804. A piece of work can be done by Ram and Shyam in 12 days, by Shyam and Hari in 15 days and by Hari and Ram in 20 days. Ram alone will complete the work in

A. 30 days

B. 32 days

C. 36 days

D. 42 days

Explanation :

(Ram’s + Shyam’s) 1 day’s work = 1/12

(Shyam’s + Hari’s) 1 day’s work = 1/15

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(Hari’s + Ram’s) 1 day’s work = 1/20

2 (Ram’s + Shyam’s + Hari’s 1 day’s work = 1/12 + 1/15 + 1/20

= (5+4+3)/60 = 1/5

∴ (Ram’s + Shyam’s + Hari’s) 1 day’s work = 1/10

∴Ram’s 1 day’s work

= 1/10 - 1/15 = (3-2)/30 = 1/30

∴ Ram alone will do the work in 30 days.

805. 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?

A. 4 days

B. 5 days

C. 6 days

D. 7 days

Explanation :

3 men = 5 women

6 men + 5 women = 15 women

∴ By M1 D1 = M2 D2

5 × 12 = 15 × D2

D2 = (5 * 12)/15 = 4 days.

806. Pipe A can fill a tank in 30 mins and Pipe B can fill it in 45 mins. If both are opened together, then after how much time must B be turned off so that the tank gets filled in 24 mins.

A. 9 mins

B. 12 mins

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C. 6 mins

D. 18 mins

Explanation :

Work done by pipe A is 24 mins = 24/30 = 4/5

This means work left for B is 1/5. B can fill the entire tank in 45 mins. So now it has to fill only 1/5 of it which should take 45/5 = 9 mins.

807. The difference of perimeter and diameter of a circle is X unit. The diameter of the circle is

A. X/(π - 1) unit

B. X/(π + 1) unit

C. X/π unit

D. (X/π - 1) unit

Explanation :

If the diameter of the circle be d units, then

π d – d = X

⇒ d(π - 1) = X

=> d = X/(π - 1) units

808. A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel party filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is just completely submerged in water, then the rise of water level in the cylindrical vessel is

A. 2 cm

B. 1 cm

C. 3 cm

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D. 4 cm

809. A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is

A. 5%

B. 7%

C. 2%

D. 1%

Explanation :

If the CP of goods be Rs. 100, then

Marked Price = Rs. 120

Hence, S.P. = (120 x 85)/100 = Rs. 102

Therefore, Gain Percent = (102 - 100)*100/100

=> Gain Percent = 2%

Hence, option C is the answer.

810. A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is

A. 45 : 56

B. 50 : 61

C. 90 : 97

D. 99 : 125

Explanation :

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CP of the book = Rs. X

Printed price = Rs. Y

Therefore, (y * 90)/100 = x * 112/100 => x/y = 90/112 = 45/56.

811. A can do a work in 60 days and B can do the same work in 40 days. They work together for 12 days and then 'A' goes away. In how many days will 'B' finish the remaining work?

A. 16 days

B. 20 days

C. 25 days

D. 28 days

E. 24 days

Explanation :

Work done by A and B in 12 days is

= 12 * 5/120 = 1/2

Therefore Remaining work = 1- 1/2 = 1/2work

B does 1/40 work in one day

Therefore B does 1/2 work in 40*1/2 =20days

812. 32 49 83 151 287 559?

A. 1118

B. 979

C. 1103

D. 1120

E. None of these

Explanation :

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32 49 83 151 287 559 ?

+17 +34 +68 +136 +272 +544

+17 +34 +68 +136 +272

So answer is 559 + 544 = 1103.

813. 462 552 650 756 870 992?

A. 1040

B. 1122

C. 1132

D. 1050

E. None of the Above

Explanation :

462 552 650 756 870 992

+90 +98 +106 +114 +122 +130

+8 +8 +8 +8 +8

So next number is 992 + 130 = 1122.

814. The average age of a woman and her daughter is 42 years. The ratio of their ages is 2 : 1 respectively. What is the daughter's age?

A. 28 years

B. 48 years

C. 52 years

D. 31 years

E. None of these

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Explanation :

Let the age of mother be M and that of her daughter be D Therefore, [M+D]/2 = 42 [M/D]=2/1 and Solving the abvoe equations we get D = 28 yrs.

815. The price of sugar is increased by 25%.Find by how much percent the consumption of sugar be decreased so as not to increase the expenditure?

A. 25%

B. 40%

C. 20%

D. 30%

E. None of these

Explanation :

Using the formula to calculate % decrease as [R/(100+R)]x100 where R = percentage increase in price, we get

Required % decrease in consumption = 25/125 MULTIPLIED 100 = 20%.

816. A car travels a distance of 45 km at the speed of 15 km/hr. It covers the next 50 km of its journey at the speed of 25km/hr and the last 25 km of its journey at the speed of 15 km/hr. What is the average speed of the car?

A. 40 km/hr

B. 24 km/hr

C. 15 km/hr

D. 18 km/hr

E. None of these

Explanation :

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We know, Average speed = Total distance travelled / Total time taken Average = [45+50+25]/[3+2+{25/15}] = 18 kmph

817. A car travels a distance of 170 km in 2 hours partly at a speed of 100 km/h and partly at 50 km/h. The distance travelled at a speed of 50 km/h is?

A. 50 km

B. 40 km

C. 30 km

D. 60 km

E. None of these

Explanation :

Suppose he covers x km at 100 kmph

So he covers 170-x at 50 kmph

So {X/100}+{170-X}/50=2

Solving this equation, we get x = 140.

So he covers 30km at 50 kmph.

818. Even after reducing the marked price of a transistor by Rs. 32, a shopkeeper makes a profit of 15%. If the cost price be Rs. 320, what percentage of profit would he have made if he had sold the transistor at the marked price?

A. 25%

B. 20%

C. 10%

D. 15%

E. None of these

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Explanation :

.Let x be the marked price,

So x - 32 = 320 X 1.15

x = 400.

So required value is

400 = 320 (1 + profit/100),

So profit is 25%

819. The ratio of the present ages of A and B 9 : 5. Five years earlier the ratio of their was 2 : 1. What is the average of their present ages?

A. 20 years

B. 25 years

C. 35 years

D. 40 years

E. None of these

Explanation :

A/b=9/5; i.e. 5a = 9B ..........(i)

A-5/B-5 = 2/1; i.e. A-5 = 2B .........10

∴A - 2B = -5 ...................(ii)

From equation (i) and (ii), A = 45, B = 25

∴ Average =45+25/2 = 70/2 = 35.

820. 20 boys and 32 girls form a group for social work. During their membership drive same no. of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 3:4 respectively?

A. 75

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B. 86

C. 68

D. 82

E. None of The above

Explanation :

Let x be the new boys as well as girls , Therefore

[20+X]/[32+X]=3/4

Solving this we get x = 16

So total will be 36 + 48 = 84.

1. (364 + 514 - ?) ¸ 4 = 200

A. 62

B. 82

C. 78

D. 68

E. 72

Explanation :

(364 + 514 - x) ¸ 4 = 200

= 878 – x = 200 × 4 => x = 878 – 800 = 78.

821. In the month of March, Hiten spent 45% of his monthly salary on paying bill and rent. Out of the remaining salary, he invested 60% in PPF and the remaining he deposited in bank. He deposited Rs. 15,400 in bank. If in April, he got an increment of 10%, what was his salary in April?

A. Rs. 84,000

B. Rs. 77,000

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C. Rs. 1,10,000

D. Rs. 59,000

E. Rs. 68,000

Explanation :

Let the initial salary of Hiten be ‘S’. Then:

(0.55 × 0.4) S = 15400 => S = 70000

After increment, Hiten’s salary = 1.1 × 70000 = 77000.

822. A person covers a certain distance by travelling at a uniform speed of 120 km/h for 90 minutes. At what speed will he have to travel in order to cover the same distance in 1 hour 20 minutes? (in km/h)

A. 135

B. 125

C. 140

D. 130

E. 145

Explanation :

Distance = 120 × 90/60 = 180 km

Speed required to cover 180 km in 1 hr 20 mins ( 4/3 hrs) =

180 × ¾ = 135 km/hr.

823. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What will be the weight of the new person?

A. 76

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B. 76.5

C. 85

D. 80

E. 90

Explanation :

Increased wt. of 8 persons = 8 × 2.5 = 20 kg

=>wt. of new person = 65 + 20 = 85 kg.

824. 50% of a number is 18 less than two-third of that number. Find the number?

A. 123

B. 115

C. 119

D. 108

E. 101

Explanation :

Let the no. be x

Given : 50x/100 = 2x/3 – 18

½ x – 2/3 x = - 18

=> x = 108.

825. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648

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B. 1800

C. 2700

D. 2000

E. 3080

Explanation :

let the no of bottles be 'B'.Using chain rule:

(6*1)/270 =(10*4)/B => B = 1800.

826. A boat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream? (in km/hr)

A. 10

B. 6

C. 5

D. 4

E. 15

Explanation :

Speed of boat = 15 km /hrs .

let the speed of stream be 's'

Given : (30/ 15+s )+ (30 /15- s) = 9/2

solving we get ,s = 5 km/hrs

827. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's present age?

A. 16 years

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B. 18 years

C. 20 years

D. 22 years

E. 25 years

Explanation :

let the age of kunal and sagar be k and s respectively

Given : k - 6 / s -6 =6/5 => 5k -6s = -6..........(1)

and : k+4 /s +4 = 11/10 =>10k - 11s =4..........(2)

Solving (1)&(2) we get s =16 years.

828. A number X is 150 more than a second number, Y. If the sum of X and Y is 5 times Y, what is the value of Y.

A. 50

B. 40

C. 80

D. 60

E. 70

Explanation :

X = 150 + Y

X + Y = 5Y

150 + 2Y = 5Y

150 = 3Y => Y = 50.

DIRECTIONS for the question 834 : Solve the following question approximately and mark the best possible answer. You are not expected to find the exact value.

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829. 39% of 129 - 43% of 97 = ?

A. 14

B. 15

C. 17

D. 9

Explanation :

129×39/100 = 50.3

97×43/100 = 41.7

? = 50.3-41.7 ≈ 9

830. 39% of 129 - 43% of 97 = ?

A. 14

B. 15

C. 17

D. 9

Explanation :

129×39/100 = 50.3

97×43/100 = 41.7

? = 50.3-41.7 ≈ 9

831. 84.99 × 18.98 ÷ 7.2 + 62.7 = ?

A. 390

B. 340

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C. 287

D. 240

Explanation :

? = 85×19 ÷ 7.2 + 62.7

= 85 × 2.64 + 62.7

= 224.3 + 62.7 = 287

832. Find the value of Square root of ( √36.1 + √28.9 ).

A. 3.4

B. 4.2

C. 4.5

D. 2.8

Explanation :

√36.1 = 6

√28.9 = 5.4

6 + 5.4 = 11.4

√11.4 = 3.4

833. 56.5% of 286 + 45.8% of 435 = ?

A. 85

B. 75

C. 361

D. 125

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Explanation :

286 × 56.5/100 = 161.6

435 × 45.8/100 = 199.2

? = 161.6 + 199.2 ≈ 361

834. 9.71 × 52.8 ÷ 50.8 + 83.4 = ?

A. 93.58

B. 103.1

C. 53.7

D. 108.4

Explanation :

? = 9.71 × 52.8 ÷ 50.8 + 83.4

= 10.1 + 83.4 = 93.5

835. A man crosses a stationary bus in 8 seconds. The same bus crosses a pole in 4 seconds. What is the respective ratio between the speed of the bus and the speed of the man ?

A. 9 : 2

B. 9 : 4

C. 18 : 5

D. Cannot be determined

E. None of these

Explanation :

Length of bus / Speed of Man = 8, Length of bus / Speed of Bus = 4

Dividing both we get Speed of bus / Speed of Man = 8/4 = 2 : 1.

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As this is not given in any of the options, the answer will be none of these.

836. An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …. , 9. But the slip on which the code is hand-written allows confusion between top and bottom, because these are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?

A. 25

B. 75

C. 80

D. 95

E. None of these

Explanation :

Total number of two digit codes that can be formed is 10 x 10 = 100.

Out of them 0, 1, 6, 8, 9 can create confusion.

Using these five digits total number of two digit numbers that can be made is 5 x 5 = 25.

But out of these 25 numbers 00,11,88,69 and 96 will not make any confusion.

Hence answer is 100 - 25 + 5 =80

837. A nine digit number is made by using the digits 1,2,3,4,5,6,7,8,9 such that digits can be repeated. Find the probability that this number is divisible by 4?

A. 2/91

B. 81/921

C. 2/9

D. 1/81

E. None of these

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Explanation :

Favourable cases = 18 (12, 16, 24, 28, 32, 36, 44, 48, 52, 56,

64, 68, 72, 76, 84, 88, 92, 93)

Required probability = (18 x 97)/99 =18/81 = 2/9

838. A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to

A. 20

B. 5

C. 30

D. 35

E. None of these

Explanation :

The total volume of the matter = (20 x 55 x 65).

Let the number of pages in the new format be n.

Hence the volume will be (65 x 70 x n).

Since the volume remains same we can equate the two and hence n = 15.71 = 16 sheets.

Hence percentage reduction in sheet = 4/20 = 20%.

839. Three distinct numbers are selected from 1st 100 natural numbers. The probability that all the three numbers are divisible by both 2 and 3 is…

A. 2/1155

B. 4/1155

C. 6/47

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D. 56/1155

E. None of these

Explanation :

A number is divisible by 2 and 3 if it is divisible by 6.

There are 16 multiple of 6 till 100.

⇒ Required probability = 16C3/100C2=4/1155

840. A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow?

A. 5/33

B. 5/22

C. 7/22

D. 7/33

E. 7/66

Explanation :

Probability of getting 1st blue ball = 7/12

Probability of getting 2nd blue ball = 6/11

So, probability of getting no yellow ball = 7/12 × 6/11 = 7/22

841. A die is thrown twice. What is the probability of getting a sum 7 from both the throws?

A. 5/18

B. 1/18

C. 1/9

D. 1/6

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E. 5/26

Explanation :

Cases of getting a sum of 7 = (1,6), (2,5), (3,4), (6,1), (5,2), (4,3) = 6

Total cases = 36

Required probability = 6/36 = 1/6

DIRECTIONS for the question 842 to 844: Read the information given below and answer the question that follows.

In a team there are 240 members (males and females). Two-third of them are males. Fifteen percent of males are graduates. Remaining males are non-graduates. Three-fourth of the females are graduates. Remaining females are non-graduates.

842. What is the difference between the number of females who are non-graduates and the number of males who are graduates?

A. 2

B. 24

C. 4

D. 116

E. 136

Explanation :

Males ⇒ 160

Females ⇒ 80

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Difference between the number of females who are non-graduates and the number of males who are graduates = 24 – 20 = 4.

843. What is the sum of the number of females who are graduates and the number of males who are non-graduates?

A. 184

B. 96

C. 156

D. 84

E. 196

Explanation :

Sum of the number of females who are graduates and the number of males who are non-graduates = 60 + 136 = 196

844. What is the ratio between the total number of males and the number of females who are non-graduates?

A. 6 : 1

B. 8 : 1

C. 8 : 3

D. 5 : 2

E. 7 : 2

Explanation :

Total number of males = 160

Number of females who are non-graduates = 20

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Required ratio = 160 : 20 = 8 : 1.

Hence, second option is the answer.

845. The product of a two-digit number and a number consisting of the same digits written in the reverse order is equal to 2,430. Find the numbers.

A. 45, 54

B. 65, 56

C. 52, 25

D. None of these

Explanation :

1st is the correct answer because 45 54 = 2430.

846. There is a natural number which becomes equal to the square of a natural number when 100 is added to it, and to the square of another natural number when 168 is added to it. Find the number.

A. 189

B. 69

C. 156

D. 224

Explanation :

3rd option is correct because 100 + 156 = 256 (square of 16)

and 168 + 156 = 324 (square of 18).

847. A and B are two stations 1000 km. A train starts from A at 70 km/h and another train starts from B at same time at the rate of 30 km/h. How far from A will they cross each other?

A. 700 km.

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B. 300 km

C. 70 km

D. 200 km

E. None of these

Explanation :

Total distance = 1000 km, Relative speed = 70 + 30 = 100 km/h.

Time after which the train will meet.1000/100 -10hours.

In 10 hour train A will cover distance = 70 * 10 = 700 km.

848. Two cyclist A and B starts from same place at the same time, one going towards east at a rate of 20 km /h and another towards west at a rate of 10 km/h what time will they take to be 75 km apart.

A. 3 hour

B. 2.5 Hours

C. 2 Hours

D. 3.25 Hours

E. None of these

Explanation :

Relative speed = 20+10 = 30 km/h, Distance to be covered = 75 km Time taken to cover that distance = 75/30 = 5/2 hour = 2.5 hour.

849. A person covers half of his journey at 30 km/hr and the remaining half at 20 km/hr. The average speed for the whole journey is

A. 18 km/hr

B. 28 km/hr

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C. 32 km/hr

D. 20 km/ hr

E. 24 km/hr

850. A person covers a certain distance by travelling at a uniform speed of 120 km/h for 90 minutes. At what speed will he have to travel in order to cover the same distance in 1 hour 20 minutes? (in km/h)

A. 135

B. 125

C. 140

D. 130

E. 145

Explanation :

Distance = 120 × 90/60 = 180 km

Speed required to cover 180 km in 1 hr 20 mins

( 4/3 hrs) = 180 × ¾ = 135 km/hr

851. In Jar A, 120 litres milk was mixed with 24 litre water. 12 litre of this mixture was taken out and 3 litre water was added. If 27 litre of newly formed mixture is taken out, what will be the resultant quantity of water in the jar? (In litre)

A. 20

B. 10

C. 15

D. 30

E. 25

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Explanation :

Ratio of milk : water in Jar A = 120 : 24 = 5 : 1

12 lts of this mixture is taken out => milk = 5/6 × 12 = 10

lts and water = 2 lts taken out

3 lts of water added = 24 – 2 + 3 = 25

lts => new ratio of milk : water = 110 : 25 = 22 : 5

Now 27 lts of this mixture is again taken out

=> water taken out = 5/27 × 27 = 5 lts water left = 25 – 5 = 20 lts

852. A boat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream? (in km/hr)

A. 10

B. 6

C. 5

D. 4

E. 15

Explanation :

Speed of boat = 15 k/h

Let the speed of stream be ‘S’

Given : 30/(15+S) + 30/(15-S) = 9/2

Solving we get, S = 5 km/h

853. 39% of 129 - 43% of 97 = ?

A. 14

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B. 15

C. 17

D. 9

Explanation :

129×39/100 = 50.3

97×43/100 = 41.7

? = 50.3-41.7 ≈ 9

854. 84.99 × 18.98 ÷ 7.2 + 62.7 = ?

A. 390

B. 340

C. 287

D. 240

Explanation :

? = 85×19 ÷ 7.2 + 62.7

= 85 × 2.64 + 62.7

= 224.3 + 62.7 = 287

855. Cost price of each of the articles A and B is Rs. X. Article A was sold at a profit of 10% and article B was sold at a profit of 30%. If the overall profit earned after selling both the articles is Rs. 136/-, what is the value of 'X'?

A. Rs 340

B. Rs 300

C. Rs 360

D. Rs 380

E. Rs 320

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Explanation :

Given : 0.1x + 0.3x = 136 => x = 340

856. Population of a village increased by 5% from 2007 to 2008 and by 25% from 2005 to 2009. If the population of the village was 480 in 2007, what was its population in 2009?

A. 640

B. 610

C. 630

D. 620

E. 650

Explanation :

Population in 2007 = 480

In 2008 = 1.05 × 480 = 504

In 2009 = 1.25 × 504 = 630

857. 400 + 206 × 12 = x

A. 2800

B. 6666

C. 4666

D. 2400

E. 2872

Explanation :

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400 + 206 × 12 = x

=> x = 400 + 2472 = 2872

858. 430% of 25 + 75% of 430 = ?

A. 340

B. 860

C. 516

D. 86

E. 630

Explanation :

430% of 25 + 75% of 430 = x 430/100 ( 25 + 75 ) => x = 430

859. There is a natural number which becomes equal to the square of a natural number when 100 is added to it, and to the square of another natural number when 168 is added to it. Find the number.

A. 189

B. 69

C. 156

D. 224

E. None of these

Explanation :

Try by options. 3rd option is correct because 100 + 156 = 256 (square of 16) and 168 + 156 = 324 (square of 18).

No other option is satisfying the 2nd condition.

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860. In a rectangular auditorium, chairs are arranged in rows and columns. The number of chairs in each column is more than the number of chairs in each row by 5. If there are in all 300 chairs, find the number of chairs in each row and in each column.

A. 25,20

B. 30,10

C. 23,18

D. 25,12

E. None of these

Explanation :

Go by options. When there were 300 chairs, so product of chairs in rows and chairs in columns should be 300. Difference of 5 should be there between the seats in rows and columns. So no option out of 1st 3 is satisfying the conditions. So answer is 4th option and correct values are 20 and 15.

861. A person sets to cover a distance of 12 km in 45 minutes. If he covers of the distance in of time, then what is the speed in the remaining time?

A. 16 km/hr

B. 8 km/hr

C. 12 km/hr

D. 55 km/hr

E. 10 km/hr

Explanation :

Distance already covered = = 9 km, Time spent = min = 30 min Distance left = (12 – 9) km = 3 km, Time left = (45 – 30) min = 15 min ∴ Required speed = 3/(5/16) km/hr = 12 km/hr.

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862. If a train 110 metres in length passes a man walking at the rate of 6 km/hr against it in 6 seconds, It will pass another man walking at the same speed in the same direction in time of

A. 9 1/3sec

B. 10 2/3sec

C. 8 sec

D. 6 sec

E. 7 1/3 sec

Explanation :

Let the speed of the train = x km/hr. Relative speed = (x + 6) km/hr = (x + 6)* 5/18 m/sec. ∴ (x + 6) * 5/18 * 6 = 110 ∴x = 60. ∴ Speed of train = 60 km/hr for 2nd person, Relative speed = (60 – 6) km/hr = 54 * 5/18 m/sec = 15 m/hr.∴Time taken to cross 2nd person = 110/15 = 22/3 = 7 1/3 sec.

863. The number of ways in which letters of the word PRAISE be arranged

A. 720

B. 610

C. 360

D. 210

E. None of these

Explanation :

Reqd. number of ways = 6! = 720.

864. Product of two co-prime numbers is 117. Then their L.C.M. is

A. Rs 3

B. Rs 39

C. Rs 117

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D. Rs 9

Explanation :

HCF of two prime numbers =1

∴ Product of numbers = HCF * LCM

LCM = 117

865. The diameters of two circles are the side of a square and the diagonal of the square respectively. The ratio of the areas of the smaller circle and the larger circle is

A. √2 : √3

B. 1 : √3

C. 1 : 2

D. 1 : 4

Explanation :

Side of square = x units

Diagonal of square =√2x units

Radius of smaller circle =x/2 units

Radius of larger circle =√2x/2=x/√2 units

⇒ Required ratio of areas = π(x2/4).π(x2/2)

= 2 : 4 = 1 : 2

866. The total surface area of a sphere is 8π square unit. The volume of the sphere is

A. (8√3)π cubic unit

B. (8√3/5)π cubic unit

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C. (8√2/3)π cubic unit

D. (8/3) π cubic unit

867. A and B together can complete; a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in

A. 8 days

B. 10 days

C. 12 days

D. 6 days

Explanation :

(A+B)’s 1 day’s work = 1/12

(B+C)’s 1 day’s work = 1/20

(C+A)’s 1 day’s work = 1/15

On adding all there, 2(A+B+C)’s day’s work = (1/12)+(1/20)+(1/15)=1/5

⇒(A+B+C)’s 1 day’s work = 1/10

Hence, the work will be finished in 10 days.

868. A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days. B alone could do the work in

A. 6 days

B. 8 days

C. 10 days

D. 4 days

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Explanation :

(A+B)’s 2 day’s work = 2/3

Remaining work = 1- (2/3)= 1/3

Time taken by A in 1/3 doing work = 2 days

Time taken by A in completing the work = 6 days

B’s 1 day’s work = (1/3)-(1/6)= 1/6

B alone will complete the work in 6 days

869. A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in

A. 6 hours

B. 8 hours

C. 10 hours

D. 4 hours

Explanation :

Efficiency of A and B = 4 : 5

Ratio of respective time = 5 : 4

⇒Time taken by B = (4/5)*(15/2)= 6 hours

870. A rational number between 3/4 and 3/8 is

A. 16/9

B. 9/16

C. 12/7

D. 7/3

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Explanation :

3/4 = (3 * 4)/(4 * 4) = 12/16 3/8 = 6/16 ⇒ 6/16,7/16,8/16,9/16,10/16,11/16,12/16 ⇒ Required rational number = 9/16.

8. The number of ways in which letters of the word PRAISE be arranged

A. 500

B. 1200

C. 200

D. 700

Explanation :

Let the prices of school bag and shoes is 7x and 5x.

Given that 7x - 5x = 200 ⇒ 2x = 200 ⇒ x = 100.

So the price of a pair of shoes = 5x = 5 * 100 = 500

871. A sum of Rs. 300 is divided among P, Q and R in such a way that Q gets Rs. 30 more than P and R gets Rs. 60 more than Q. The ratio of their share is

A. 3 : 2 : 5

B. 2 : 5 : 3

C. 5 : 3 : 2

D. 2 : 3 : 5

Explanation :

Q = P + 30 ⇒ Q – P = 30 and R – Q = 60 = 2 × 30

⇒Required ratio = 2 : 3 : 5

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Look : 3 – 2 = 1, 5 – 3 = 2

872. The average of nine numbers is 50. The average of first five numbers is 54 and the average of last three numbers is 52. What will be the value of sixth number?

A. 24

B. 44

C. 30

D. 34

Explanation :

The sixth number = 9 * 50 – 5 * 54 – 3 * 52 = 450 – 270 – 156 = 24.

873. The average of the first nine integral multiples of 3 is

A. 15

B. 18

C. 21

D. 12

Explanation :

Required average = 3(1+2+3+...+9)/9 = (9 * 10)/(2*3) = 15

874. An article is sold for Rs. 300 at a profit of 20%. Had it been sold for Rs. 235, the loss percentage would have been

A. 5

B. 6

C. 16

D. 3

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Explanation :

C.P. of the article = (100/120)*130 = Rs. 250 On selling at Rs. 235, Loss percent = (15/250)*100 = 6%

875. A box has 100 blue balls, 50 red balls, 50 black balls. 25% of blue balls and 50% of red balls are taken away. % of black balls at present is

A. (100/3)%

B. 40%

C. 50%

D. 25%

Explanation :

After taking away respective balls, the number of balls in the box = 75 + 25 + 50 = 150. Number of black balls = 50. Now the percentage of black balls = 100*50/150 = 33.33%, the first option.

876. A dozen pairs of socks quoted at Rs. 180 are available at discount of 20%. How many pairs of socks can be bought for Rs. 48?

A. 2 pairs

B. 5 pairs

C. 3 pairs

D. 4 pairs

Explanation :

⇒ S.P. of a dozen pairs of socks = (180* 80)/100 = Rs.144

⇒ S.P. of 1 pair of socks = 144/12 = 12

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⇒ No. of pairs available for Rs. 48 = 48/12 = 4.

877. The marked price of a table is Rs. 12,000. If it was sold for Rs. 10,500 after allowing a certain discount, then the rate of discount is

A. 112.5%

B. 15%

C. 17.5%

D. 10%

Explanation :

Discount = 12000 - 10500 = 1500.

Now the percentage discount is = 100 *1500/12000 = 12.5%

Hence first option is the answer.

878. The marked price of a radio set is Rs. 480. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be

A. 18.5%

B. 20%

C. 25%

D. 18%

Explanation :

If the C.P. of ratio be SR. X then

If no discount is allowed,

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Gain = 480 – 400 = Rs. 80 Gain percent =

879. N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is

A. 26/7 cm

B. 72/7 cm

C. 47/7 cm

D. 86/7 cm

880. Two cars are moving with speeds v1, v2 towards a crossing along two roads. If their distances from the crossing be 40 meters and 50 metres at an instant of time then they do not collide if their speeds are such that

A. v1 : v2 ≠ 5 : 4

B. v1 : v2 = 25 : 16

C. v1 : v2 = 16 : 25

D. v1 : v2 ≠ 4 : 5

Explanation :

If 40/V1= 50/V2 ,then they will collide i.e. cars will reach at the same time

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881. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds is:

A. 1:4

B. 2:1

C. 1:2

D. 4:1

Explanation :

If the original speed be S1 units and time = 11 units and distance = D, then (D/2)/2t1= S2

⇒ S2 = D/4t1

and S1= D/t1

882. The sum of the dimensions of a room (i.e. length, breadth and height) is 18 metres and its length, breadth and height are in the ratio of 3 : 2 : 1 respectively. If the room is to be painted at the rate of Rs. 15 per m2, what would be the total cost incurred on painting only the four walls of the room (in Rs.)?

A. 3250

B. 2445

C. 1350

D. 2210

E. 2940

Explanation :

Ratio of length : breadth : height = 3 : 2 : 1

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Breath = 2/6×18 = 6

Height = 1/6×18 = 3

Area of four walls = 2h×(l+b) = 2×3(9+6) = 90

Total cost of painting four walls = 90×15 = 1350

883. B is 4/3 times as efficient as A. If A can complete 5/8th of a given task in 15 days, what fraction of the same task would remain incomplete if B works on it independently for 10 days only?

A. 3/4

B. 2/3

C. 5/8

D. 4/9

E. 2/3

Explanation :

B is 4/3 times as efficient of A.

Ratio of time taken by A and B, A: B is 4:3.

A can complete 5/8th of a given task in 15 days

A can do alone his work in = 8/5× 15= 24 days

Therefore, B can do this work= 18

B works independently for 10 days only, thus work done = 10/18 = 5/9

Remaining work (incomplete) = 1-5/9 = 4/9

884. In a class, the average weight of boys is 64 kg and that of 75 girls is 70 kg. After a few days, 60% of the girls and 30% of the boys leave. What would be the new average weight of the class (in kg)? Assume that the average weight of the boys and the girls remain constant throughout.

A. 63

B. 66.5

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C. 68.5

D. 65.5

E. Can't be determined

Explanation :

In this question, number of boys is not mentioned .So, we can’t find new average.

885. 382 380 374 356 302 ?

A. 212

B. 240

C. 140

D. 201

E. 158

Explanation :

The pattern is as follows:

382 – 2 = 380

380 – 6 = 374

374 – 18 = 356

356 – 54 = 302

302 – 162 = 140

886. 3 9 45 315 ? 31185

A. 2465

B. 2685

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C. 2955

D. 2835

E. 2785

Explanation :

The pattern is as follows:

3 * 3 = 9

9 * 5 = 45

45 * 7 = 315

315 * 9 = 2835

887. 12 14 18 26 42 ?

A. 106

B. 74

C. 92

D. 68

E. 84

Explanation :

The pattern is as follows:

12 + 2 = 14

14 + 4 = 18

18 + 8 = 26

26 + 16 = 42

42 + 32 = 74

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888. In how many ways can 3 integers be selected from the set {1, 2, 3, …….., 37} such that sum of the three integers is an odd number?

A. 3876

B. 7638

C. 6378

D. 1938

E. 969

Explanation :

There are 18 even and 19 odd numbers in the given set. For sum to be odd either all 3 numbers should be odd or 2 of them even and one odd. This is possible in 19C3 + (18C2 × 19C1) = 3876 ways

889. There are 13 married couples, 5 single men and 7 single women in a party. Every man shakes hand with every woman once, but no one shakes hand with his wife. How many handshakes took place in the party?

A. 247

B. 347

C. 360

D. 191

E. 100

Explanation :

Any single man will have = 13 + 7 = 20 options.

Total number of handshakes by single men = 20 × 5= 100. Any married man will have 12 + 7 = 19 options.

Total number of handshakes by married men = 19 × 13 = 247. Total number = 247 + 100 = 347.

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890. A and B are two towns. A car goes from A to B at a speed of 64 km/hr and return to A at a slower speed. If its average speed for the whole journey is 56 km/hr, it returned with speed

A. 152.54 km/hr

B. 47.52 km/hr

C. 49.78 km/hr

D. 53 km/hr

E. 57 km/hr

Explanation :

Let the speed on the return journey be x km/hr. Then, 56 = = 7(64 + x) = 16x or 9x = 448 ∴ x = 448/9 = 49.78 km/hr.

891. A train travels 225 km in 3.5 hours and 370 km in 5 hours. Find the average speed of train.

A. 80 km/hr

B. 60 km/hr

C. 70 km/hr

D. 63 km/hr

E. 50 km/hr

Explanation :

Here, x1 = 225, x2 = 370, T1 = 3.5 and T2 = 5.

∴ Average speed of train = (X1 + X2)/(T1 + T2) = (225+370)/(3.5+5) = 70 km/hr.

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892. The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that

A. AP x BP = CP x DP

B. AP x CP = AB x CP

C. BP x AB = CD x CP

D. AP x CP = BP x DP

Explanation :

Here, AC and BD are chords of the circle so AP x PC = BP x PD.

893. If tan Θ = 3/4 and Θ is acute, then cosec Θ is

A. 5/4

B. 4/3

C. 4/5

D. 5/3

Explanation :

tan Θ=3/4

cot Θ = 4/3

cosec2Θ - cot2Θ = 1

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cosec Θ= √ 1+cot2Θ = √ 1+(4/3)2 = √1+16/9=√25/9=5/3

894. If O be the circum centre of a triangle PQR and ∠QOR = 110 °, ∠OPR = 25 °, then the measure of ∠PRQ is

A. 55 °

B. 60 °

C. 65 °

D. 50 °

Explanation :

∠QOR = 110 ° ∠OPR = 250 ° ∠QPR = 110 ° / 2 = 55 ° OR = OP ∠OPR = ∠PRO = 25° ∠OQR = ∠ORQ = 70/2 = 35 ° PRQ = 25 ° + 35 ° = 60 °

895. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40m long on the ground. The height of the tower is

A. 65m

B. 70m

C. 72m

D. 60m

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Explanation :

height of Tower/Length Of Stick

h/12=40/8

h=40*12/8 = 60 metre

896. A, B, C, D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 1300 and ∠ECD = 200. ∠BAC is

A. 100 °

B. 110 °

C. 120 °

D. 90 °

Explanation :

∠BEC = 130 °

∠DEC = 180 ° - 130 ° = 50 °

∠EDC = 180 °-50 ° -20 ° = 110 °

∠BAC = ∠EDC = 110 °

(Angle on the same arc)

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897. In a triangle, if three altitudes are equal, then the triangle is

A. Right

B. Isosceles

C. Obtuse

D. Equilateral

Explanation :

The only possible case is when the Triangle is equilateral.

898. The tops of two poles of height 24m and 36 m are connected by a wire. If the wire makes an angle of 60 ° with the horizontal, then the length of the wire is

A. 8 m

B. 6 √3 m

C. 6 m

D. 8√3m

Explanation :

DE = 36-24 = 12 metre

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=8√3 metre

899. The value of 1/cosecΘ-cotΘ-1/sinΘ is

A. Cosec Θ

B. tan Θ

C. 1

D. cot Θ

900. The sum of the squares of the digits constituting a two-digit number is 10, and the product of the required number by the number consisting of the same digits written in the reverse order is 403. Find the number.

A. 13

B. 31

C. 41

D. Both 1 & 2

E. None of these

901. The product of a two-digit number and a number consisting of the same digits written in the reverse order is equal to 2,430. Find the numbers.

A. 45,54

B. 65,56

C. 52,25

D. 35,53

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E. None of these

Explanation :

Try by options. 1st is the correct answer because 45*54 = 2430.

902. A garrison of 750 men has provisions for 20 weeks. If at the end of 4 weeks, they are re-inforced by 450 men, how long will the provision last?

A. 8 weeks

B. 12 weeks

C. 14 weeks

D. 15 weeks

E. 10 weeks

Explanation :

750*20 = 750*4+1200*W =>W = 10 weeks

903. If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap the same field in 36 days?

A. 540 hectares

B. 450 hectares

C. 420 hectares

D. 489 hectares

E. None of these

Explanation :

H = 80*36/8*36/24= 540 hectares

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904. A person covers half of his journey at 30 km/hr and the remaining half at 20 km/hr. The average speed for the whole journey is

A. 18 km/hr

B. 28 km/hr

C. 32 km/hr

D. 20 km/ hr

E. 24 km/hr

Explanation :

Here, s1 = 30 and s2 = 20.therefore Average speed = =2*30*20/30+20 = 24 km/hr.

905. Rajesh covers a certain distance by bus at 16 km/hr and return back at the starting point on a cycle at 9 km/hr. His average speed for the whole journey is

A. 13.54 km/hr

B. 11 km/hr

C. 15.52 km/hr

D. 11.52 km/hr

E. None of these

Explanation :

Here, s1 = 16 and s2 = 9.therefore Average speed = = 2*16*9/16*9= 11.52 km/hr.

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906. 430% of 25 + 75% of 430 = ?

A. 430

B. 860

C. 516

D. 86

E. 630

Explanation :

430% of 25 + 75% of 430 = x

430/100 ( 25 + 75 ) => x = 430

907. Approximate value of Square root of 2412 – 1592= ?

A. 320

B. 75

C. 150

D. 180

E. 210

908. (364 + 514 - ?)/4=200

A. 162

B. 82

C. 78

D. 68

E. 72

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Explanation :

(364 + 514 - x)/4 = 200

= 878 – x = 200 × 4 => x = 878 – 800 = 78

909. The difference between S.I and C.I on certain of money for 3 years at 10% per annum is Rs. 248. Find the sum?

A. 2000

B. 8000

C. 16000

D. 4000

E. None of these

Explanation :

Let us consider sum of money is Rs. 1000. S.I. =1000*10*3/100= 300 C.I. = 1000(1+10/100)3 – 1000 = 331 Difference between SI and CI = 331 – 300 = 31 Rs. 31 is difference, when sum = Rs. 1000 Rs. 248 is Difference, then sum =1000*248/31= 8000

910. The average score of a cricketer for 13 matches is 42 runs. If his average score for the first 5 matches is 54, then what was his average score (in runs) for last 8 matches?

A. 37

B. 39

C. 34.5

D. 33.5

Explanation :

Total Score = Average * Number of matches

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Total score of 13 matches = 13 × 42 = 546

Total score of first 5 matches = 5 × 54 = 270

Therefore, total score of last 8 matches = 546 - 270 = 276

Average = 276/8 = 34.5

Hence the answer is option C

911. If the graphs of the equations x + y = 0 and 5y + 7x = 24 intersect at (m, n), then the value of m +n is

A. 2

B. 1

C. 0

D. -1

Explanation :

By solving the given two equations, we get the intersection point (12, - 12).

So, m = 12, n = -12

Hence, m + n = 12 – 12 = 0 So, ans. is option C.

912. A function f(x) is defined as f(x) = f(x – 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?

A. 0

B. 89

C. -89

D. None of these

Explanation :

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Let S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6)

As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1)

f(2) = f(0) - 8

f(3) = f(1) - 15

f(4) = f(2) - 24 = f(0) - 32

f(5) = f(3) - 35 = f(1) - 50

f(6) = f(4) - 48 = f(0) - 80

Put the above values in equation (1), we get

S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80

S = 2(f(0) + f(1)) - 153 ------ (2)

As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32

Putting this value in equation 2, we get S = 2(32) - 153 = -89

So, Ans is option C.

913. What annual payment will discharge a debt of Rs. 6,450 due in 4 years at 5% per annum simple interest?

A. 1400

B. 1500

C. 1550

D. 1600

E. None of these

Explanation :

Let the annual installment be rs. x

therefore (x + x*3*5/100)+(x + x*2*5/100)

+(x + x*1*5/100)+x =6450

=>115x/100+110x/100+105x/100+x=6450

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=>115x+110x+105x+100x=6450*100

=>430x=6450*100

x=6450*100/430=rs.1500

914. The average of the first 100 positive integers is

A. 100

B. 51

C. 50.5

D. 49.5

E. 49

Explanation :

n(n+1)/2

1+2+3+....+n

therefore average of these numbers=n+1/2

therefore required average

100+1/2=50.5

915. In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?

A. 12 years

B. 11 years

C. 10.5 years

D. 10 years

E. None of these

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Explanation :

Father+Mother=2*35=70 years

Father+Mother+Son=27*3=81 years

therefore Son's age=81-70=11 years

916. The length and breadth of a rectangle are increased by 20% and 40% respectively. What is the percentage increase in its area?

A. 60%

B. 68%

C. 78%

Explanation :

Apply the percentage formula. The percentage increase in the area will be P + Q + PQ / 100. So we get the answer as 20 +

40 + 20 × 40/100 = 68%. i.e. 2nd option.

917. The diameter of a circle is 21 metres. It will take how many revolutions to cover a distance of 6.6 km?

A. 80

B. 50

C. 200

D. 100*

Explanation :

No. of revolutions = Distance/circumference.

Distance = 6.6 × 1000 = 6600 metres.

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Circumference = 2 × 22/7 × 21/2 = 66 metres.

No. of revolutions = 6600/66 = 100 revolutions. i.e. 4thoption

918. There was one mess for 30 boarders in a certain hostel. If the number of boarders is increased by 10, the expenses of the mess were increased by ` 4,000 per month, while the average expenditure per head diminished by ` 200. Find the original monthly expenses.

A. Rs. 36,000

B. Rs. 41,000

C. Rs. 39,000

D. Rs. 48,000

Explanation :

Average Expenditure for 40 boarders = (x + 4000)/40. The difference = x / 30 + (x + 4000)/40 = 200. Solving x = 36000

919. In two alloys, copper and zinc are related in the ratios of 4 : 1 and 1 : 3. 10 kg of 1st alloy, 16 kg of 2nd alloy and some of pure copper are melted together. An alloy was obtained in which the ratio of copper to zinc was 3 : 2. Find the weight of the new alloy.

A. 45 kg

B. 40 kg

C. 35 kg

D. 50 kg

Explanation :

In First alloy, Ratio of copper and zinc is 4:1.

So the ratio will be 8:2 for 10 kg.

In Second alloy, Ratio of copper and zinc is 1:3

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So the ratio will be 4:12 for 16 kg.

They are mixed together to get new copper and zinc ratio 12:14

Now, because of adding pure copper, resultant ratio is 3:2 and we have 12:14 which means 2x = 14. So 3x = 21.

So, 9 kgs of pure copper should get added to get 3:2 ratio.

So total addition of mixture is 12 + 14 + 9 = 35 kg.

920. An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0-5 cm. If the sides of the sheet be in the ratio 1:5, then the sides are

A. 40 cm, 200 cm

B. 20 cm, 100 cm

C. 10 cm, 50 cm

D. None of these

Explanation :

10 cm has been hammered in 0.5 cm then

10 cm / 0.5 cm = 20.

So the smaller side will be 20 and the ratio of 1:5 becomes 20:100.

921. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 sec respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A. 78 km/h

B. 72 km/h

C. 66 km/h

D. 81 km/h

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Explanation :

If the length (in km) and speed (in km) of the train is L and St resp. We have

L / (St – 4.5) = 8.4/3600 and

L/(St-5.4) = 8.5/3600

Thus we get two equations,

3600 L = 8.4 St – 54 and

3600 L = 8.5 St – 45.9

On Equating, we get 0.1St = 8.1St

= Speed of train = 81

922. A train 300 m long is running at a speed of 90 km/h. How many seconds will it take to cross a 200 m long train running in the opposite direction at a speed of 60 km/h?

A. 12

B. 36/5

C. 60

D. 20

Explanation :

90 km/h = 90 x 5/18 m/s = 25 m/s.

60 km/h = 60 x 5/18 m/s = 50/3 m/s

T = D / S = (300+200) / (25 + 50/3) = 12 m/s.

923. A monthly fee of a student consists of a constant part and a part which varies according to the number of activity clubs he wishes to join. The fee for all activity clubs is the same. A student has to pay Rs.1,075 per month, if he enrolls in three activity clubs and Rs.950 per month, if he enrolls in two activity clubs. The total monthly bill of three students who are enrolled in four activity clubs each is

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A. Rs.2800

B. Rs.3600

C. Rs.3300

D. Rs.4800

Explanation :

For enrolling in three activities = Rs.1075

For enrolling in two activities = Rs.950

So increase of Rs.125 for 1 more activity.

Thus, for enrolling in four activities = Rs.1200

So for three students enrolling in four activities

= 3 x Rs 1200 = Rs 3600

924. In an election, a total of 9801 votes were polled. 126 votes were invalid. The successful candidate got 5 votes for every 4 votes his opponent had. At what margin did the successful candidate win his election if there were only 2 candidates?

A. 1205

B. 949

C. 1136

D. 1075

Explanation :

So total votes are distributed as 5x + 4x = 9675

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9x = 9675 => x = 1075.

925. Two water taps together can fill a tank in 75/8 hours. The tap of the longer diameter takes 10 hours less than the smaller one to fill the tank separately. The time in which the smaller tap can fill the tank separately is

A. 25 hours

B. 10 hours

C. 15 hours

D. 15/4 hours

Explanation :

Two water taps together can fill a tank in 75/3 hrs.

1/(x -10) + 1/x = 8/75 => x =15/4 or 100/4

Smaller tap can fill the tank separately in 25 hours.

926. Meena builds a circular swimming pool of radius 5 m inside a circular garden of radius 12 m. In order to compensate the area covered due to construction of pool, she extends the radius by 'r' metres keeping the garden still circular. What is the value of V?

A. 1/2 m

B. 2 m

C. 1 m

D. 4 m

927. How many kg of sugar costing Rs. 57.5 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 45 per kg so that the mixture is worth Rs. 55 per kg?

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A. 350kg

B. 300kg

C. 50kg

D. 325kg

Explanation :

(X x 57.5 + 75 x 45) / (X + 75) = 55

x = 300 kg.

928. A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. The number of cones thus formed is

A. 140

B. 132

C. 112

D. 126

Explanation :

929. If the ratio of the diameters of two right circular cones of equal height be 3: 4, then the ratio of their volumes will be

A. 3:4

B. 9:16

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C. 16:9

D. 27:64

Explanation :

930. The sum of two numbers is equal to 15 and their arithmetic mean is 25 per cent greater than their geometric mean. Find the numbers.

A. 5 & 10

B. 3 & 12

C. 1 & 14

D. 6 & 9

E. None of these

Explanation :

AM of 2 numbers is a+b/2.GM of 2 numbers is √a+b.When sum of 2

numbers is 15, their AM is 7.5. AM = 1.25 (GM)

=> GM =7.5/1.25 = 6. Hence 36 = ab. So product of 2 numbers is 36. Try by

931. The product of the digits of a two-digit number is twice as large as the sum of its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.

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A. 36

B. 27

C. 63

D. 88

E. None of these

Explanation :

Go by options. 3rd option is the answer because 63 => product of digits = 6*3 = 18.

Sum of digits = 6 + 3 = 9. Hence product of digits is twice as the sum of the digits. Also 63 – 27 = 36.

So digits are reversed.

932. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What will be the weight of the new person?

A. 76

B. 76.5

C. 85

D. 80

E. 90

Explanation :

Increased wt. of 8 persons = 8 × 2.5 = 20 kg

wt. of new person = 65 + 20 = 85 kg

933. 50% of a number is 18 less than two-third of that number. Find the number.

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A. 123

B. 115

C. 119

D. 108

E. 101

Explanation :

Let the no. be x

Given : 50x/100 = 2x/3 – 18

½ x – 2/3 x = - 18

=> x = 108

934. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648

B. 1800

C. 2700

D. 2000

E. 3080

Explanation :

Let the no. of bottles be ‘B’. Using chain rule:

(6×1)/270 = (10×4)/B => B = 1800

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935. At 60% of its usual speed, a train of length L meters crosses platform 240 meters long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in meters)?

A. 140

B. 225

C. 220

D. 480

E. 240

Explanation :

Let usual speed = S m/s.

According to the question,

60% of S=

9S= L+240………… (i)

Also given that, S = L/6

L = 6S …. (ii)

From (i) & (ii)

=> 9S= 6S+240

=> 3S= 240

S=80 m/s

From (ii)

L= 6×80 =480 m

936. Shiva gives 20% of her monthly salary to his mother, 50% of the remaining salary he invests in an insurance scheme and PPF in the respective ratio of 5 : 3 and the remaining he keeps in his bank account. If the sum of the amount he gives to his mother and that he invests in PPF is Rs. 12,600, how much is Shiva’s monthly salary?

A. Rs. 36,000

B. Rs. 64,000

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C. Rs. 42,000

D. Rs. 40,000

E. None of these

Explanation :

Let the total amount be x.

0.2x = given to mother.

0.25x= invested in insurance

0.15x= invested in ppf

0.4x= Bank account

Given, 0.2x+0.15x = 0.35x = 12600; x=36000.

937. The respective ratio of radii of two right circular cylinders (A & B) is 4 : 7. The respective ratio of the heights of cylinders A and B is 2 : 1. What is the respective ratio of volumes of cylinders A and B?

A. 25 :42

B. 23 : 42

C. 32 : 49

D. 30 : 49

E. 36 : 49

938. At present, Aanshi is five years younger to Binny. Binny’s age twenty- years hence will be equal to twice of Aanshi’s age five years ago. What will be Binny’s age eight year hence?

A. 42 years

B. 35 years

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C. 30 years

D. 48 years

E. None of these

Explanation :

Let age of Aanshi be A, Bunny be B.

According to equation, A= B-5

Also, B+20 = 2(B-10)

Solving these we get, B= 40. So 8 years hence his age will be 48 years.

939. A number is such that when it is multiplied by 6, it gives another number which is s more than 168 as the original number itself is less than 168. What is 15% of the original number?

A. 8.4

B. 7.8

C. 6.6

D. 8.8

E. 7.2

Explanation :

Let the no. be x.

Now as given, 6x - 168= 168 – x

7x = 336; x= 48

=> 0.15x = 7.2

940. Dharma invested Rs. P for 3 years in scheme A which offered 12% p.a. simple interest. She also invested Rs. P + 400 in scheme B which offered 10%

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compound interest (compounded annually), for 2 years. If the amount received from scheme A was less than that received from scheme B, by Rs. 304, what is the value of P?

A. Rs. 1400

B. Rs. 1000

C. Rs. 1500

D. Rs. 900

E. Rs. 1200

941. Percent profit earned when an article is sold for Rs. 558/- is double the percent profit earned when the same article is sold for Rs. 504/-. If the marked price of the article is 30% above the cost price, what is the marked price of the article?

A. Rs. 585/-

B. Rs. 595/-

C. Rs. 624/-

D. Rs. 590/-

E. Rs. 546/-

Explanation :

Let Percent profit be P

558 = (1+ 2P/100)CP

504 = (1+P/100)CP

Solving these equations we get, CP=Rs.450, p=12%

Now, MP=1.3*450 = Rs.585/-.

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942. Dhruva gave 35% of her monthly salary to her mother. From the remaining salary, she paid 18% towards rent and 42% she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 43,920. What was her monthly salary?

A. Rs. 80,000

B. Rs. 75,000

C. Rs. 64,000

D. Rs. 76,000

E. Rs. 72,000

Explanation :

Let ‘x’ be the monthly salary, then

(65/100 × 40/100)x + 35/100x = 43920

Solving, X= 72000

943. 18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of 2 : 1. If the resultant respective ratio of milk and water in the vessel was 4 : 1, what was the quantity of pure milk added in the vessel? (in litres)

A. 4

B. 8

C. 10

D. 12

E. 2

Explanation :

80(M) + 18(W) = 98

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49 liters sold => 49 is left

40(M) + 9(W)

Let x be the quantity of pure milk added

Given, (40 + 2x)/(9 + x) = 4/1

Solving, x = 2

944. There are two motor cycles (A & B) of equal cost price. Motorcycle A was sold at a profit of 14% and motorcycle B was sold for Rs. 4,290/- more than its cost price. The net profit earned after selling both the motor cycles (A & B) is 20%. What is the cost price of each motorcycle?

A. Rs. 16,500/-

B. Rs. 16,000/-

C. Rs. 15,500/-

D. Rs. 71,500/-

E. Rs. 17,000/-

Explanation :

Let the cost price of each motorcycle be Rs. ‘A’. So SP of A = 1.14A and SP of B = A + 4290. Total CP = 2A. As net profit is given to be 20% on both the motorcycles, so we can form the equation as (2.14A + 4290 - 2A)/2A = 20%. Solving it further, we get (0.14A + 4290)5 = 2A. Solving this equation, we get value of A as 16,500

945. A bag contains 3 white balls and 2 black balls. Another bag contains 2 white and 4 black balls. A bag and a ball are picked at random. What is the probability that the ball drawn is white?

A. 7/11

B. 7/30

C. 5/11

D. 7/15

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E. None of them

Explanation :

(3/5+2/6)×½,Solving, 7/15

946. The average age of a man and his son is 28 years. The ratio of their ages is 3 : 1 respectively. What is the man's age?

A. 30 years

B. 38 years

C. 44 years

D. 42 years

E. None of these

Explanation :

Total sum of man's age & his son's age =28 A— 2 = 56

Now, the Ratio of their ages is 3 : 1.

Therefore, Man's age = (3/4) A— 56 = 42

So, the correct answer is option D.

947. A car manufacturing plant manufactures 96 dozen cars in eight days. How many dozen cars will the plant manufacture in 17 day ?

A. 210

B. 224

C. 204

D. 209

E. None of these

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Explanation :

The plant manufactures 96 dozen cars in 8 days

that means, It manufactures 96/8 = 12 dozen cars/day

So, In 17 days, it will manufacture 17 A— 12 = 204 dozen cars

Therefore, the answer is option C.

948. A & B together can complete a piece of work in 16 days, B alone can complete the same work in 24 days. In how many days can A alone complete the same work ?

A. 34 days

B. 50 days

C. 48 days

D. 42 days

E. None of these

Explanation :

Let A alone can complete the work in x days and B alone can complete the work in 24days.

Therefore, according to the given conditions,

1/x + 1/24 = 1/16

1/x = 1/48

So, A's one day work is 1/48 which means that A will complete the entire work in 48days.

Therefore, the answer is option C.

949. Find the average of the following set of scores

142, 93, 102, 206, 115, 98

A. 122

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B. 106

C. 138

D. 117

E. None of these

Explanation :

So, average = 756/6 = 126

So, the correct answer is option E (none of these).

950. The average of four consecutive odd numbers P, Q, R and S respectively (in increasing order) is 104. What is the sum of P & S?

A. 204

B. 208

C. 206

D. 212

E. None of these

Explanation :

Let the four consecutive odd numbers P, Q, R and S be X, X+2, X+4 and X+6 respectively.

So, average = X+3 =104

=> X = 101

So P = 101 & S = 107

And Sum of S and P will be 208.

Hence, the answer is option B.

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951. If cos Θ + sin Θ = √2cos Θ, then cos Θ - sin Θ is

A. -√2 sinΘ

B. √2 sinΘ

C. √2 tanΘ

D. -√2 cosΘ

Explanation :

cosΘ + sinΘ = √2 cosΘ on squaring both sides,

cos2Θ + sin2Θ + 2 cosΘ. sinΘ =2cos2Θ

=> cos2Θ - sin2Θ = 2sinΘ, cosΘ

=> (cosΘ + sinΘ) (cosΘ - sinΘ)

= 2 sinΘ, cosΘ

=> (2 sinΘcosΘ)/ √2 cosΘ = √2 sinΘ

952. Number of students institute A & B were in the ration of 7: 15 respectively in 2012. In 2013 the no. of students in institute A increased by 25% and the no. of institute B institute B increased by 26%, then what was the respective ratio between no. of students in institutes A & B respectively in 2013?

A. 25:56

B. 24:55

C. 24:53

D. 25:53

E. 25:54

Explanation :

Let the students in institute A and B 7x,15x

In 2013

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Students in A = 5/4(7x)=35x/4

Students in B = 126/100(15x)

Required. Ratio = (35x)100/4(126)(15x) = 25/54

Hence , Option 5

953. An employer pays Rs.26/- for each day a worker works and forfeits Rs. 7/- for each day he is idle. All the end of 56 days. If the worker got Rs. 829/- for how many days did the worker remains idle?

A. 21

B. 15

C. 19

D. 13

E. 17

Explanation :

Say he works for x days

26x-7 (56-x)=829

33x=1221

x =37

As he works for 37 days so he is idle for 19 days

Hence, Option 3

954. A right pyramid stands on a square base of side10 cm. If the height of the pyramid is 12 cm, the area (in cm2) of its slant surface is

A. 520

B. 420

C. 360

D. 260

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955. If each interior angle of a regular polygon is 150°, the number of sides of the polygon is

A. 8

B. 10

C. 15

D. None of these

Explanation :

Each interior angle in a regular polygon = (n-2) x 180/n

where, n is the no of sides.

Here, (n-2) x 180/n = 150

=> 180n - 360 = 150n

=> 30n = 360

=> n = 12

So, Ans. is option D.

956. If the Altitude of a right prism is 10 cm and its base is an equilateral triangle of side 12 cm, then its total surface area ( in cm2 ) is

A. 5 + 3√3

B. 36√3

C. 360

D. 72( 5 + √3 )

957. The value of tan 10° tan 15° tan 75° tan 80° is

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A. 0

B. 1

C. -1

D. 2

Explanation :

tan10 tan15 tan75 tan80

we know that tan10 = tan(90 - 80) = cot 80o

and tan15 = tan( 90 - 75) = cot 75o

Therefore,tan10 tan15 tan75 tan80

= cot80 cot75 tan75 tan80

=1/tan80 x 1/tan75 x tan80 =1 =so,Answer is option B

958. If sin 7x = cos11x, then the value of tan 9x + cot 9x is

A. 1

B. 2

C. 3

D. 4

Explanation :

sin 7x = cos 4x

=>sin (9x-2x) = cos(9x-2x)

=>sin 9x.cos 2x - cos9x.sin2x =cos9x.cos2x -sin 9x.sin 2x

=>sin 9x.cos 2x + sin 9x.sin 2x =cos9x.cos2x +cos9x.sin2x

=>sin 9x.(cos 2x + sin 2x) = cos 9x.(cos 2x +sin 2x)

=>sin 9x/cos 9x = 1

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=>tan 9x = 1

Now,tan 9x+ cot 9x

= tan 9x + 1 /tan 9x

= 1 + 1/1 = 2

959. A person sets to cover a distance of 12 km in 45 minutes. If he covers of the distance in of time, then what is the speed in the remaining time?

A. 16 km/hr

B. 8 km/hr

C. 12 km/hr

D. 55 km/hr

E. 10 km/hr

Explanation :

Distance already covered = 3/2*12 = 9 km, Time spent = 2/3*45 min = 30 min

Distance left = (12 – 9) km = 3 km, Time left = (45 – 30) min = 15 min

Therfore, Required speed = 3/ 15/60 km/hr = 12 km/hr.

960. If a train 110 metres in length passes a man walking at the rate of 6 km/hr against it in 6 seconds, it will pass another man walking at the same speed in the same direction in time of

A. 91/3sec

B. 101/3sec

C. 8 sec

D. 6 sec

E. 7 1/3sec

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Explanation :

Let the speed of the train = x km/hr. Relative speed = (x + 6) km/hr = (x + 6) X 15/8 m/sec

(x + 6)x 5/18x6 = 110, x = 60. Speed of train = 60 km/hr for 2nd person,

Relative speed = (60 – 6) km/hr = 54x5/18 m/sec = 15 m/hr. Time taken to cross 2nd person =110/15=22/3= 7 1/3 sec.

961. The difference of two numbers is 11 and one fifth of their sum is 9. The numbers are :

A. 31,20

B. 30,19

C. 29,18

D. 28,17

Explanation :

x − y = 11, x + y = 5 × 9 x − y = 11, x + y = 45, y = 17, x = 28

962. How many numbers between 1 and 100 are divisible by 7 ?

A. 9

B. 11

C. 17

D. 14

Explanation :

No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d

98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7

98/7= N = 14

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963. Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:

A. 8 cms

B. 12 cms

C. 14 cms

D. 16 cms

964. If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be :

A. 128

B. 132

C. 133

D. 136

Explanation :

If values are proportional to 13 : 11 : 7, then the number of coins will be proportional to 13/1 : 11/0.50 : 7/0.25 ⇒ 13 : 22 : 28. Now from this the number of coins of 50 paise will be 378 × 22/63 = 132.

965. In how many ways can 3 integers be selected from the set {1, 2, 3, …….., 37} such that sum of the three integers is an odd number?

A. 3876

B. 7638

C. 6378

D. 1938

E. 969

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Explanation :

There are 18 even and 19 odd numbers in the given set. For sum to be odd either all 3 numbers should be odd or 2 of them even and one odd. This is possible in 19C3 + (18C2 × 19C1) = 3876 ways

966. The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 275, then the mean profit for the last 15 days would be

A. Rs. 200

B. Rs. 350

C. Rs. 275

D. Rs. 425

Explanation :

Average would be : 350 = (275 + x)/2 On solving, x = 425.

967. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.

A. Rs. 480

B. Rs. 520

C. Rs. 420

D. Rs. 460

Explanation :

Let d be the average daily expenditure

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Original expenditure = 35 × d

New expenditure = 35 × d + 42

New average expenditure will be :

(35 × d + 42)/42 = d - 1

On solving, we get d = 12

Therefore original expenditure = 35 × 12 = 420

968. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's present age?

A. 16 years

B. 18 years

C. 20 years

D. 22 years

E. 25 years

Explanation :

Let the ages of Kunal and Sagar be K and S respectively.

Given : (K-6)/(S-6) = 6/5 => 5K – 6S = -6 ……(i)

And: (K+4)/(S+4) = 11/10 => 10K – 11 S = 4 …..(ii)

Solving (i) & (ii) we get: S = 16 years.

969. A number X is 150 more than a second number, Y. If the sum of X and Y is 5 times Y, what is the value of Y?

A. 50

B. 40

C. 80

D. 60

E. 70

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Explanation :

X = 150 + Y

X + Y = 5Y

150 + 2Y = 5Y

150 = 3Y => Y = 50

970. 4/9 of 3/16 of 6/13 of ? = 155

A. 4420

B. 4240

C. 4320

D. 4030

E. 4120

Explanation :

971. 156.25 × 12.4 + 1.8 × 52.5 = ? – 175.85

A. 2124.5

B. 2212.6

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C. 2207.85

D. 2684.8

E. 2624.4

Explanation :

156.25×12.4+1.8×52.5=?-175.85

1937.5+94.5=?-175.85

2032=?-175.85

?=2207.85

Hence, Option C.

972.

A. 35 1/5

B. 35 5/8

C. 31 3/8

D. 32 2/5

E. 33 1/8

Explanation :

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DIRECTIONS for the questions 973 to 978 : Solve the following question and mark the best possible option.

973. S mixed 36 kg of sugar @ Rs. 45/- per kg and 24 kg of sugar @ Rs. 48/- per kg and sold the mixture as to earn 20% profit. At what rate per kg must he sell the sugar.

A. Rs. 52.56

B. Rs. 52.42

C. Rs. 52.36

D. Rs. 55.44

E. Rs. 54.25

Explanation :

Total cost price=36×45+24×48=2772/-

Average cost price per kg = 2772/60 = Rs. 46.2

S.P=Rs 55.44 per kg( @20% profit)

974. The length of a rectangle exceeds its breadth by 6m. Length of the rectangle is equal to the side of a square whose area is 729 sq. m. What is the perimeter of the rectangle? (in m)

A. 96

B. 108

C. 92

D. 88

E. 84

Explanation :

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Let ‘l’ be the length, ‘b’ be the breadth of the rectangle.

Length of the rectangle =Side of the square of area 729m2

∴ Length of the rectangle =27m. A.T.Q. l-b=6

⇒ b = l - 6 = 21m ⇒ l = 27m

Perimeter of the rectangle = 2 (l + b) = 2 (27 + 21) = 96m

Hence, Option A.

975. Raghuvir purchased 10 calculators and 16 watches for Rs. 56,100/- and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 calculators and 24 watches together so as to earn the same percent profit?

A. Rs. 1,00,980/-

B. Rs. 1,16,176/-

C. Rs. 1,21,176/-

D. Rs. 1,00,660/-

E. Rs. 1,24,132/-

Explanation :

CP of 10 calculators , 16 watches =Rs.56100/-

CP of 15 calculators, 24 watches=1.5×56100=84150/-

Profit=20%

∴S.P. of 15 calculators, 24 watches =1.2×84150 = Rs. 100,980/-

Hence, Option A.

976. Some chocolates were distributed among 4 friends A, B, C and D such that respective ratio of chocolates received by A to chocolates received by C was 7:9. B received 29 more chocolates than A and D received 33 more chocolates than C. If B received 15 more chocolates than C, how many chocolates did D receive?

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A. 84

B. 96

C. 72

D. 99

E. 87

Explanation :

A=7x, C=9x, B=7x+29, D=9x+33

A.T.Q. 29 + 7x =15+9x

⇒ x = 7

Hence, Option B.

977. Abhijit invested an amount with company X for two years @ simple interest rate 15 p.c.p.a. The entire amount obtained from company X after two years he invested with company Y @ compound interest rate 12 p.c.p.a for two years. If the amount finally received by him was Rs. 81,536. Find the money invested by abhijit in company X.

A. Rs. 65,000/-

B. Rs. 60,000/-

C. Rs. 56,000/-

D. Rs. 50,000/-

E. Rs. 45,000/-

Explanation :

Let ‘y’ be the invested amount

A.T.Q.

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1.3y(1.12)2=81536

On Solving y=Rs.50,000/-

∴Hence, Option D.

978. Average weight of 40 students in a class is 55 kg. Six of them whose average weight is 52 kg left the class and another set of six students, whose average weight is 42kg joined the class. What is the next average weight of the class (in kg?)

A. 54.25

B. 52.75

C. 53.5

D. 54

E. 53

Explanation :

New Average weight = (40 * 55 - 60)/40 = 53.5 kg

Hence, Option C.

978. The ratio of roses and lilies in a garden is 3: 2 respectively. The average number of roses & lilies is 180. What is the number of lilies in the garden?

A. 144

B. 360

C. 182

D. 216

E. None

Explanation :

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Let the number of so be ‘3x’ and the number of lilies be 2x

Average number of roses and lilies = (3x + 2x)/2 = 2.5x

A.T.Q

2.5x = 180, x = 72

Number of lilies = 2x = 144. Hence, Option A

979. Salaries of A, B and C are in the ratio 4 : 5 : 9. If their salaries are increased by 25%, 10% and 50% respectively, what will be the new ratio of their salaries?

A. 6:5:13

B. 10:11:27

C. 5:6:15

D. 11:20:27

E. None of these

Explanation :

Let their original salaries be 4k, 5k and 9k.

Now, new salaries are 1.25 4k : 1.15k : 1.59k = 5k : 5.5k : 13.5k = 10:11:27

980. The ratio of the present ages of A and B 9 : 5. Five years earlier the ratio of their was 2 : 1. What is the average of their present age

A. 20 years

B. 25 years

C. 35 years

D. 40 years

E. None of these

Explanation :

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let present age of A=9x

So present age of B=5x

According to question

9x-5/5x-5=2/1

solving this we get,

x=5 so average is 45+25/2=35 years.

981. A Shopkeeper wants to earn 12% profit on an item after giving 20% discount to the customer. By what percentage should he increase his marked price to arrive at the label price?

A. 24%

B. 32%

C. 40%

D. 16%

Explanation :

Let the current price be Rs. 100.

For getting 12% profit he should sell it at Rs. 112.

Let the label price be x.

i.e. he need to increase 40% on label price

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982. A can do a work in 60 days and B can do the same work in 40 days. They work together for 12 days and then A goes away. In how many days will B finish the remaining work?

A. 16 days

B. 20 days

C. 25 days

D. 28 days

E. 24 days

Explanation :

Work done by A and B in 12 days is

=12(1/60+1/40)=12 * 5/120=0.5

Remaining work = 1- [0.5]=0.5 work

B does 1/40 work in one day

so B does 0.5 work in 40 * 0.5 days = 20 days

983. A train crosses platforms of length 160 meters and 220 metres in 16 seconds and 20 seconds respectively. What is the length of the train?

A. 60 metres

B. 175 metres

C. 80 metres

D. 100 metres

E. 120 metres

Explanation :

Let the length of the train 'x' and speed of train be 'V' ms-1.

{160+x}/16={220+x}/20=V

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{160+x}/4={220+x}/5

800+5x=880+4x;

5x-4x=880-800

x=80 metres

984. 8423 + 3120 + 6543) / (1536 + 377 + 189) =?

A. 5.8

B. 14.6

C. 8.6

D. 18.3

E. 17.2

Explanation :

(8423+3120+6543) is nearly equal to 18000

& (1536+377+189) is nearly equal to 2100.

So required answer is (18000) /2100 = 8.6.

985. (13% of 7439) * (3.23 % of 537) =?

A. 16243

B. 14002

C. 18674

D. 19874

E. 16774

Explanation :

first we calculate 13% of 7439

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10% of 7439 = 744 & its 3% is nearly 224 therefore 13% of 7439 = 744 + 224 = 968.

Similarly 3.23 % of 537 = 16.2 + 1 = 17.2. So we get answer as 17.2 x 968 = 16660 (approx).

Hence option E is the answer.

986. (15.28 x 3.56) /3.15=?

A. 12

B. 9

C. 68

D. 17

E. 42

Explanation :

3.56/3.15=1 app.

So answer will be little above than 15 so answer is 17

987. 93 + 26 * 3 - 51 = ?

A. 201

B. 102

C. 120

D. 210

E. None of these

Explanation :

93 + 26 * 3 - 51 = 93 + 78 - 51 = 171 - 51 = 120

988. 63 * 9 * 14 /? = 98

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A. 83

B. 86

C. 88

D. 91

E. None of these

Explanation :

Let the missing number be x Then 63 * 9 * 14 /x = 98 63 * 9 * 14=98 x = 63 * 9 * 14/98=81 So, the correct answer is option E.

989. 7[1/3]+ 5[4/9]-4[4/9]=?

A. 8[7/9]

B. 8[1/3]

C. 8[2/3]

D. 8[5/9]

E. None of these

Explanation :

7[1/3]+5[4/9]-4[4/9]=7+5-4+[1/3+4/9-4/9]=8[1/3]

990. 6[3/8]+3[2/7]+9[7/8]=?

A. 19[13/28]

B. 15[19/28]

C. 19[15/28]

D. 15[13/28]

E. None of these

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Explanation :

(6+3+9)+(3/8+2/7+7/8)=19[15/28]

991. If the area of a rectangle is 1248 square meters and its breadth is 32 meters how much is its perimeter?

A. 142 meters

B. 128 meters

C. 148 meters

D. 124 meters

E. None of these

Explanation :

Length of rectangle = area /breadth So, length will be 1248/32 = 39 Perimeter will be 2 (length + breadth) = 2 (39 + 32) = 142 meters.

992. What will be the compound interest on a sum of Rs. 7200/- at 5 p.c.p.a. in 2 years?

A. Rs. 841/-

B. Rs. 738/-

C. Rs.793/-

D. Rs. 812/-

E. Rs. 694/-

Explanation :

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993. In how many different ways can the letters of the word 'PARTY' be arranged?

A. 120

B. 2005

C. 2400

D. 720

E. None of these

Explanation :

Total no. of ways =5 * 4 *3 *2 *1 = 120

994. Cost of 68 pens and 96 pencils is Rs. 788/-. What is the cost of 17 pens and 24 pencils?

A. Rs.193/-

B. Rs.189/-

C. Rs 197/-

D. Rs. 183/-

E. None of these

Explanation :

Cost of 68 pens and 96 pencils = 788/-

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Cost of 17 pens and 24 pencils = 788/4 = 197/-

995. 5 10 25 70 205 ?

A. 650

B. 670

C. 550

D. 610

E. None of these

Explanation :

5 10 25 70 205 ?

+5 +15 +45 +135 +405

*3 *3 *3 *3

So, the missing term is 205 + 405 = 610

996. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?

A. l hour

B. 1 hour 40 minutes

C. 1 hour 20 minutes

D. 2 hours 40 minutes

Explanation :

Water flowed in 1 hour through the pipe

=22/7 * 10*10*3000/10000 meter3

=660/7 meter3

Volume of circular/cylindrical cistern

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=660/7 * 5*5*2 = 1100/7 meter3

= Required Time = 1100/7/660/7 = 5/3 hours

= 1 hour 2/3 * 60 minutes

= 1 hour 40 minutes

997. A bicycle wheel makes 5000 revolutions in moving 11 km. The diameter of the wheel, in cm, is

A. 35

B. 55

C. 65

D. 70

Explanation :

Distance covered by wheel in one revolution = 2Πr

∴ 5000 × 2Πr = 11 × 1000

⇒ 5000 × 2 × 22/7 × r = 11000

⇒ r =11000*7 / 5000*2*22 = 0.35 metre

= 35 cm

∴ Diameter

= 2 × radius = 2 × 35 = 70 cm

998. At each corner of a triangular field of sides 26 m, 28 m and 30 m, a cow is tethered by a rope of, length 7 m. The area (in m2) ungrazed by the cows is

A. 336

B. 259

C. 154

D. 77

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999. A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains Rs. 56 on one item, his advertised price of the item, in Rs., is

A. 820

B. 780

C. 790

D. 800

Explanation :

Let the advertised price be Rs. x. ∴ S.P. = Rs. 77x/100

∴ C.P. = Rs(77x/100 - 56)

⇒ 77x -5600/100 =(100/110 * 77x/100)

⇒77x -5600/100 = 7x/10

⇒ 7x -5600 = 70x ⇒ 7x = 5600 ⇒ x = Rs. 800

1000. The average of 25 observations is 13. It was later found that an observation 73 was wrongly entered as 48. The new average is

A. 12.6

B. 14

C. 15

D. 13.8

Explanation :

Difference of two observations = 73 - 48 = 25

∴ New average = 13 + 25/25 = 14

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1001. If the cost price of 10 articles is equal to the selling price of 8 ar¬ticles, then gain per cent is

A. 10%

B. 8%

C. 50%

D. 25%

Explanation :

Profit percent= 10-8/8 × 100 = 25%

1002. An article is marked 40% above the cost price and a discount of 30% is allowed. What is the gain or loss percentage?

A. 10% gain

B. 5% gain

C. 2% loss

D. 12% loss

Explanation :

Let the C.P. of article be Rs. 100. ∴ Marked price = Rs. 140 S.P. = 70% of 140 = Rs. 98

8. A man bought oranges at the rate of 8 for Rs. 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs. 45?

A. 90

B. 100

C. 135

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D. 150

Explanation :

Let the man buy 24 (LCM of 8 and 12) oranges. ∴ C.P. of 24 oranges = 34/8 × 24 = Rs. 102 S.P. of 24 oranges = 57/12 × 24 = Rs. 114 Gain= 114- 102 = Rs. 12 ∵ Rs. 12≡ 24 oranges ∴ Rs. 45 ≡ 24/12 × 45 = 90 oranges

1003. The number 0.121212.... in the form p/q is equal to

A. 4/11

B. 2/11

C. 4/33

D. 2/33

Explanation :

0.121212 …. = 0.12 = 12/99 =4/33

1004. Simple interest on Rs. 1200 @ 13 p.c.p.a. for 'X' years is Rs. 624/-. What is the amount on Rs. 'X+1000' at the same rate of interest for 3 years?

A. Rs. 1872/-

B. Rs. 1384/-

C. Rs. 936/-

D. Other than those given as options

E. Rs. 1404/-

Explanation :

624 = (1200×13×x)/100 => x = 4 Now, P = x + 1000 = 4 + 1000 = 1004 I = (1004×13×3)/100 = 392 => amount = 1004 + 392 = 1396/-

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1005. P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of what Q has. If P, Q and R together have Rs. 240 then how much money does P alone have? (in Rs.)

A. 75

B. 60

C. 120

D. 80

E. 90

Explanation :

Assume that P has 2x amount. Therefore, Q = 3x amount (50% more than P) And R = 3x ×1/3= x Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1 Thus, P alone have = (2/6) × 240 = Rs. 80

1006. Bill, Simon, and John are brothers, given Simon is the eldest. Bill is as many years younger than one brother as he is older than the other. Simon is 7 years younger than twice the age of John. John is 5 years older than half the age of Bill. What is the sum of the ages of Bill, Simon and John?

A. 12

B. 24

C. 48

D. Can’t say

E. None of these

Explanation :

S – B = B – J

J = B/2 + 5.

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S = 2J – 7.

S = B + 10 – 7 = B + 3.

J = B/2 + 5. 2S = B + 10.B/2 + 5 + B + 3 = 2B. B/2 = 8. B = 16, S = 19, J = 13. So B + S + J = 16 + 19 + 13 = 48.

1007. The sum of the squares of the digits constituting a two-digit number is 10, and the product of the required number by the number consisting of the same digits written in the reverse order is 403. Find the number.

A. 13

B. 31

C. 41

D. Both 1 & 2

E. None of these

Explanation :

1st condition is satisfied by 1st and 2nd options. 2nd condition is also satisfied by both these options because (1)2 + (3)2 = 10 and (3)2 + (1)2 = 10. Also 31 * 13 = 403 and 13*31 = 403. S the answer is 4th option.

1008. A circle and rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What will be the area of the circle? (in cm2)

A. 88

B. 1250

C. 154

D. 128

E. Other than those given as options

Explanation :

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Perimeter of rectangle = perimeter of circle = 2 (18 + 26) = 88 2πr = 88 => r = 14cm Area of circle = 22/7 ×14 × 14 = 616 cm2

1009. Some men promised to do a job in 18 days, but 6 of them became absent and remaining men did the job in 20 days. What is the original number of men?

A. 50 men

B. 60 men

C. 65 men

D. 70 men

E. 55 men

Explanation :

Let the number of men originally = M. According to the given condition M => 18 = ( M – 6) => 20 => M = 60

1010. The number of ways in which 8 persons can be seated at a round table if 2 particular persons must always sit together

A. 288

B. 720

C. 1440

D. 2880

E. None of these

Explanation :

Reqd. number of ways = 2! × (7 – 1)! = 2! × 6! = 1440.

1011. The number of ways in which 7 boys and 8 girls can be seated in a row so that they are alternate

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A. 203121800

B. 29030400

C. 3628800

D. 203212800

E. 3628800

Explanation :

Reqd. number of ways = 7! × 8! = 203212800.

1012. 50% of a number is 18 less than two-third of that number. Find the number.

A. 123

B. 115

C. 119

D. 108

E. 101

Explanation :

Let the no. be x

Given : 50x/100 = 2x/3 – 18

½ x – 2/3 x = - 18

=> x = 108

1013. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648

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B. 1800

C. 2700

D. 2000

E. 3080

Explanation :

Let the no. of bottles be ‘B’. Using chain rule:

(6×1)/270 = (10×4)/B => B = 1800

1014. In a 200 meters race, A beats B by 20 meters, while in a 100 meters race, B beats C by 5 meters. A beats C in a kilometer race by

A. 105 meters

B. 225 meters

C. 205 meters

D. 145 meters

Explanation :

When A = 200, B = 180.

When B = 100, C = 95.

Make B = 900. A will be 1000. C will be 855.

1015. A person purchases tomatoes from each of the 4 places at the rate of 1 kg, 2 kg, 3 kg, 4 kg per rupee respectively. On an average he has purchased x kg of tomatoes per rupee. Then the value of x is

A. 2

B. 2.5

C. 1.92

D. None of these

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Explanation :

x = 10/4 = 2.5

1016. A sum of money doubles itself in 7 years. In how many years it becomes four fold?

A. 35 years

B. 28 years

C. 14 years

D. 21 years

Explanation :

Double in seven years.

So 4 times will be in = 7 × (4 − 1) = 21 years.

1017. A fast train takes 3 hours less than a slow train for a journey of 600 km, If the speed of the slow train is 10 km/hr less than that of the fast train, the speeds of the two trains are

A. 60 km/hr and 70 km/hr

B. 50 km/hr and 60 km/hr

C. 40 km/hr and 50 km/hr

D. 30 km/hr and 40 km/hr

Explanation :

(600/x)-(600/x+10)=(3/1)

Solving this, we get x = 40

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1018. When 75% of a number is added to 75, the result is the same number. The number is

A. 150

B. 300

C. 100

D. 450

Explanation :

Let the number be equal to x.

3x/4 +75 = x

Hence x=300

1019. If 5 spiders can catch five flies in five minutes, how many flies can hundred spiders catch in 100 minutes?

A. 100

B. 1000

C. 500

D. 2000

Explanation :

5 × 5 × x = 100 × 100 × 5 ⇒ x = 2000.

1020. A car travels 25km an hour faster than a bus for a journey of 500km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are

A. 25km/hr and 40km/hr respectively

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B. 25km/hr and 60 km/hr respectively

C. 25km/hr and 50km/hr respectively

D. None of these

Explanation :

Let the speeds of bus and car be x and y. Here, y = x +25

As per the question, (500/x)-(500/x+25)=10

⇒ 500(x + 25) − 500(x) =10x(x+25) ⇒ x = 25, y = 50.

For such questions, you can also use direct substitution from the given choices

1021. An article is bought for Rs. 600 and sold for Rs. 750. The gain percent is:

A. 20%

B. 25%

C. 30%

D. None

1022. If P : Q = 3 : 4 and Q : R = 5 : 6, then P : Q : R is:

A. 3 : 4 : 6

B. 3 : 5 : 6

C. 15 : 20 : 24

D. 5 : 6 : 3

Explanation :

P:Q=3:4, Q:R=5:6, P:Q:R=3×5:5×4:6×4

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⇒ 15:20:24

1023. Two years ago the average age of a family of 8 members was 18 years. After the addition of a baby, the average age of family remains the same today. What is the age of the baby ?

A. 1 year

B. 2 years

C. 4 years

D. 3.5 years

1024. An article when sold at a gain of 5% yields Rs. 15 more than when sold at a loss of 5%. The cost price of the article is:

A. Rs. 200

B. Rs. 150

C. Rs. 80

D. Rs. 64

Explanation :

10/100 × x = 15 ⇒ x=150

As the loss and profit both are earned on the cost price.

1025. If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be:

A. Rs. 300

B. Rs. 200

C. Rs. 240

D. Rs. 350

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Explanation :

Z share = Z,

Y = 1.2Z

X = 1.25×1.2Z,

X+Y+Z =740

(1.25× 1.2+1.2+1)Z=740

3.7Z=740, Z=200

1026. In a mixture of 35 litres the ratio of milk and water is 4 : 1. If 7 litres of water is added to the mixture, the ratio of milk to water in the resultant mixture will become :

A. 2 : 3

B. 3 : 2

C. 2 : 1

D. 1 : 2

Explanation :

Mixture = 35L, Milk = 4/5 × 35 =28L

Water = 1/5 × 35 =7L

New 28/7+7 = M/W

⇒ 28/14 = M/W =2/1

1027. What will be the income tax payable by a person getting a taxable income of Rs. 30,000 during the year if the first Rs. 18000 is not taxable and the tax rates are 25% of the next Rs. 12000 ?

A. Rs. 3000

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B. Rs. 3250

C. Rs. 3500

D. Rs. 3750

Explanation :

T.I.=30,000, N.T.I.=18000

Taxable 12000, Income Tax = 25% of Taxable Income

= 1/4 ×: 12000 = RS.3000

1028. 10 men can finish a piece of work in 10 days whereas it takes 12 women to finish it in 10 days. If 15 men and 6 women undertake to complete the work, how many days will they take to complete the work?

A. 2

B. 4

C. 5

D. 11

Explanation :

10 men = 10 days, 1 men 1 day = 1/100 work

12 women = 12 days, 1 women 1 day = 1/120

15 men + 6 women, 15 × 1/100 + 6 × 1/120

3/20 +1/20= 4/20 =1/5 work= 5 days

1029. A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is:

A. 20%

B. 18%

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C. 16%

D. 12%

Explanation :

Let the CP = 100 Rs.

Mark Price = 140

Discount = 20%

Selling price 80/100 × 140 = 112

Hence profit = 12%

1030. A train 280 metres long is moving at 60 kms per hour. The time taken by the train to cross a platform 220 metres long is:

A. 20 seconds

B. 25 seconds

C. 30 seconds

D. 35 seconds

1031. A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:

A. 4000

B. 6000

C. 8000

D. 10000

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Explanation :

Total expenditure = 40 + 25 + 15 + 5 = 85%

Saving = (100 - 85) = 15%

15/100 × Salary = 1200, Salary = 8000 Rs.

1032. 11.7 * 4.1 - 5.97 = ?

A. 48

B. 42

C. 46

D. 39

E. None of these

Explanation :

11.7 * 4.1 - 5.97 = 47.97 - 5.97 = 42

1033. The value of 1/cosecΘ-cotΘ-1/sinΘ is

A. Cosec Θ

B. tan Θ

C. 1

D. cot Θ

Explanation :

Expression = 1/cosec Θ - cot Θ - 1/cosec Θ cosec2Θ-cot2Θ/cosecΘ-cotΘ-cosecΘ =cotΘ (cosec2Θ - cot2Θ-1; 1/sinΘ = cosecΘ)

1034. In a triangle, if three altitudes are equal, then the triangle is

A. Right

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B. Isosceles

C. Obtuse

D. Equilateral

Explanation :

The only possible case is when the Triangle is equilateral.

1035. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs 300 more. The sum is

A. 5300

B. 5500

C. 5000

D. None of these

Explanation :

Increase of 3% fetched Rs.300 more. It is for 2 years. For 1 year Increase of 3% will fetch Rs.150. So 1 % will fetch Rs.50 100% = 5000.

1036. A sum of Rs 1,550 was lent partly at 5% and partly at 8% per annum simple interest. The total interest received after 3 years was Rs 300. The ratio of money lent at 5% to that lent at 8% is

A. 5:8

B. 8:5

C. 31:6

D. 16:15

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Explanation :

Partly division of 1550 is x and x - 1550 5 % of x + 8 % of (1550 – x) = 0.05x + 0.08(1550 – x) For 3 years, the total interest is 300. 3[0.05x + 0.08(1550 – x)] = 300 x = 800 and 1550 – x = 750 The ratio of money = 16:15.

1037. The cost price of item B is Rs. 150/- more than the cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?

A. Rs. 450/-

B. Rs. 420/-

C. Rs. 400/-

D. Rs. 350/-

E. Rs. 480/-

Explanation :

Let us assume cost price of A= X

So that Cost price of B= X+150.

SP of A= X*1.1

SP of B=(X+150)*0.8

Given that

SPA: SPB

11:12

So that 1.1X/(X+150)*0.8= 11/12

X=300

CP of B= 300+150

1038. A vessel contains a mixture of milk and water in the respective ratio of 10 : 3. Twenty-six litres of this mixture was taken out and replaced with 8 litres of

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water. If the resultant respective ratio of milk and water in the mixture was 5 : 2, what was the initial quantity of mixture in the vessel? (in litres)

A. 143

B. 182

C. 169

D. 156

E. 130

Explanation :

26 L mixture is taken out.

Quantity of Milk is taken out= 26*(10/13)=20

Quantity of Water is taken out=26*(3/13)=6

As we know that,

(10X-20)/(3X-6+8)=5/2

X=10,

Initial quantity of mixture in the vessel is= 13*X=13*10=130L.

1039. There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number?

A. 31

B. 27

C. 29

D. 25

E. 33

Explanation :

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Let the 6 consecutive odd no.’s are :

X, X+2, X+4,X+6, X+8, X+10

Avg. of 1st three no’s is X+2.

Avg. of Last three no’s is X+8.

Given that (X+8)2-(X+2)2=288

X=19

Last odd no. is X+10= 29.

1040. In a bag there are 6 red balls and 9 green balls. Two balls are drawn at random, what is the probability that at least one of the balls drawn is red?

A. 29/35

B. 7/15

C. 23/35

D. 2/5

E. 19/35

Explanation :

Probability of atleast one of the balls drawn is red= 1- (9/15)*(8/14)=23/35. Answer is 23/35.

1041. 81% of 4915 = ?

A. 3819.15

B. 3871.15

C. 3981.15

D. 3918.15

E. None of these

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Explanation :

81/100*4915=3981.15

1042. 1682 /58 * ? = 377

A. 13

B. 15

C. 16

D. 14

E. None of these

Explanation :

Let the missing number =X

Then 1682/58*x=377

x=377*58/1682=13

1043. A started a business by investing Rs. 25000. At the end of 4th month from the stat of the business B joined with Rs. 15000 and at the end of 6th month from the start of the business, C joined with Rs. 20000. If the A’s share in profit at the end of year was Rs. 7,750, what was the total profit received?

A. Rs. 13,950

B. Rs. 13,810

C. Rs. 13,920

D. Rs. 12,780

E. Rs. 14,040

Explanation :

A = 25000*12 , B = 15000*8, C = 20000*6

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Ratio = A:B:C = 5:2:2. Let TP be the total profit.

Given, 5/9 * TP = 7750 => TP = 13950.

1044. The respective ratio of radii of two right circular cylinders (A & B) is 3 : 2. The respective ratio of volumes of cylinders A and B is 9 : 7, then what are the heights of cylinders A and B?

A. 8 : 5

B. 4 : 7

C. 7 : 6

D. 5 : 4

E. 6 : 5

1045. (512/?) *(39/16)*328=128

A. 3199

B. 3168

C. 3189

D. 3188

E. None of these

Explanation :

Let missing number be x then (518/x)*(39/16)*328=128

X= (512*39*328)/(16*128)=3198 So, the correct answer is option E.

1046. The cost price of an article is Rs. 7950/-. If it is to be sold at a profit of 18%, how much would be its selling price ?

A. Rs. 9431/-

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B. Rs. 9183/-

C. Rs. 9218/-

D. Rs. 9381/-

E. None of these

Explanation :

SP={(100+profit%)/100}*Cost price

SP={(100+18%)/100}*7950=9381

1047. The ratio of the ages of A and B is 4:3 respectively. The ratio of their ages eight years from now will be 6:5 respectively. How old was A, when B was 7 years old?

A. 16 years

B. 11 years

C. 9 years

D. 12 years

E. None of these

Explanation :

Let the ages of A and B be 4x and 3x respectively.

now after 8 years their ages will be 4x+8 and 3x+8

then according to question (4x+8)/(3x+8)=6/5 Then x will be 4.So present age of B is 12 and present age of A is 16.

So when B was 7 years old, A was 11 years old.

1048. The sum of three consecutive even numbers is 1434. What is the largest number ?

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A. 438

B. 484

C. 476

D. 472

E. None of these

Explanation :

The sum of three consecutive even numbers is 1434

So, their average will be 1434/3 = 478, which is also the middle no.

So, maximum no. will be 478 + 2 = 480.

Therefore, the correct answer is option E.

1049. ? 7800 1560 390 130 65

A. 47120

B. 49900

C. 46800

D. 48350

E. None of these

Explanation :

The series pattern is: 65×2= 130,

130 ×3= 390,

390×4= 1560,

1560 ×5= 7800,

7800×6= 46800.

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1050. 7 35 210 ? 6300 31500

A. 1040

B. 1060

C. 1080

D. 1030

E. None of these

Explanation :

Pattern is *5, *6, *5, *6, *5.

Following the same, the answer should be 210 * 5 = 1050.

So, the correct answer is option E.

1051. A boat takes a total time of twelve hours to travel 105 kms upstream and the same distance downstream. The speed of the boat in still water is six times of the speed of the current. What is the speed of the boat in still water? (In km/hr)

A. 12

B. 30

C. 18

D. 24

E. 36

Explanation :

Let ‘x’ be the speed of Boat in still water, and ‘y’ be the speed of current.

Then, according to the question,

Speed of the boat in still water = 6 speed of current

x = 6y

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Also given that ,

105/(x+y) +105/(x-y) =12

105/7y +105/5y =12

12y=36

y=3

Therefore, x= 6×3=18

Speed of the boat in still water= 18kmph

1052. At 60% of its usual speed, a train of length L meters crosses platform 240 meters long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in meters)?

A. 440

B. 425

C. 220

D. 480

E. 240

Explanation :

Let usual speed = S m/s.

According to the question,

60% of S= (L+240)/15

9S= L+240………… (i)

Also given that, S = L/6

L = 6S …. (ii)

From (i) & (ii)

9S= 6S+240

3S= 240

S=80 m/s

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From (ii)

L= 6×80 =480 m

1053. P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of

A. 75

B. 60

C. 120

D. 80

E. 90

Explanation :

Assume that P has 2x amount.

Therefore, Q = 3x amount (50% more than P)

And R = 3x × 1/3 = x

Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1

Thus, P alone have = (2/6) × 240 = Rs. 80

1054. Suri gave 25% of her monthly salary to her mother. From the remaining salary, she paid 15% towards rent and 25%, she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 42000. What was her monthly salary?

A. Rs. 50,000

B. Rs. 60,000

C. Rs. 65,000

D. Rs. 64,000

E. Rs. 72,000

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Explanation :

Let x be the total income

(75/100*60/100)x + 25/100x = 42000

Solving, x = 60000

1055. At present, Ami’s age is twice Dio’s age and Cami is two years older than Ami. Two years ago, the respective ratio between Dio’s age at that time and Cami’s age at that time was 4: 9. What will be Ami’s age four years hence?

A. 40 years

B. 30 years

C. 42 years

D. 36 years

E. 48 years

Explanation :

D; A = 2D; C = A+2 = 2D+2

Given, D-2/(2D+2)-2 = 4/9

Solving, D = 18 Years and A = 36+4 = 40 years.

1056. If tan Θ = 3/4 and Θ is acute, then cosec Θ is

A. 5/4

B. 4/3

C. 4/5

D. 5/3

Explanation :

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tan Θ=3/4

cot Θ = 4/3

cosec2Θ - cot2Θ = 1

cosec Θ= √ 1+cot2Θ = √ 1+(4/3)2 = √ 1+16/9 = √ 25/9 =5/3

1057. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40m long on the ground. The height of the tower is

A. 65m

B. 70m

C. 72m

D. 60m

Explanation :

height of Tower/Length Of Stick

h/12=40/8

h=40*12/8 = 60 metre

1058. 40.1% of 360.2 + 58.98% of ? = 150

A. 10

B. 20

C. 30

D. 40

E. 50

Explanation :

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40*360+59%of X=150

144+59%of X=150

X=10(approx)

1059. 96.894 + 33.002 + 15.02 * 7.99 = ?

A. 180

B. 250

C. 140

D. 269

E. 170

Explanation :

97+33+15*8=250

1060. (42.11×5.006)-√17×15.08=?

A. 250

B. 150

C. 45

D. 200

E. 125

Explanation :

(42*5)-4*15=150

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1061. The sum of a number and the two numbers preceding it is equal to 30. Find the number:

A. 10

B. 11

C. 9

D. 8

Explanation :

Number is 9,

As 9 +10+11=30

1062. Sanjay invested an amount of Rs 16,000 for two years on compound interest and received an amount of RS 17,640 on maturity. What is the rate of interest per annum?

A. 4%

B. 5%

C. 8%

1063. Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there?

A. 2

B. 4

C. 3

D. 5

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Explanation :

x / 9 – y / 6 = 1/9;

2x – 3y = 2

We can compute that x = 4 and y = 2.

Thus, Inlet pipe = x = 4.

1064. A reservoir is provided by two pipes A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in

A. 12 hours

B. 8 hours

C. 10 hours

D. 11 hours

Explanation :

If x is the speed then speed of A= x + 5 and B = x

Time taken by A and B will be x and x + 5 resp.

1/x + 1/x + 5 = 1/6 ; x2 – 7x - 30 = 0 x = -3 or x = 10.

Since time can’t be negative, x =10.

1065. A dealer buys dry fruits at the rate of ` 100, ` 80 and ` 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain or no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity?

A. 30%

B. 40%

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C. 20%

D. 50%

Explanation :

Total quantity rate =

(12 * 100 + 15 * 80 + 20 * 60) = 3600

For first 2 quantity, (12 * 100) + (15 * 80) = 2400

But he gets 20% profit = 2400 * 1.2 = 2880

So the third quantity = 3600 – 2880 = 720

Actual third quantity rate = 20 * 60 = 1200

Loss suffered = (1200 - 720) / 1200

= 480/1200 = 40 %

1066. How many kgs of flour worth Rs 25 per kg must be blended with 30 kgs of flour worth Rs 30 per kg so that by selling the blended variety at Rs 30 per kg there should be a gain of 10%?

A. 32 kg

B. 40 kg

C. 36 kg

D. 42 kg

Explanation :

(25X+30×30 )/(X+30)=300/11

X=36

1067. A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the

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stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B?

A. 200 km

B. 180 km

C. 160 km

D. 220 km

Explanation :

Speed of boat for downstream = 14 + 4 = 18 km/hr

Speed of boat for upstream = 14 – 4 = 10 km/hr

Distance = x

x / 18 + (x /2)/10 = 19

x = 180 km

1068. The speed of a boat in still water is 4 km/h and the speed of current is 2 km/h. If the time taken to reach a certain distance upstream is 9 hours, the time it will take to go the same distance downstream is

A. 3.5 hours

B. 2.5 hours

C. 2 hours

D. 3 hours

Explanation :

Upstream speed of a boat = 4 – 2 = 2 km/hr

Downstream speed of a boat = 4 + 2 = 6 km/hr

Suppose time taken = x

Then for Upstream case: 9 = x / 2 So, x = 18 km

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Now for downstream case :Time = 18/6 = 3 hrs

1069. In a stream running at 2 km/h, a motor boat goes 10 km upstream and back again to the starting point in 55 min. The speed of the motorboat in still water is

A. 22 km/h

B. 21 km/h

C. 20 km/h

D. 24 km/h

Explanation :

Let "x" be the speed of Motor boat in still water

Distance = 10 km; Time = 55/60 hrs

For upstream, the speed of motorboat = x - 2

For downstream, the speed of motorboat = x + 2

55 / 60 = 10/ (x – 2) + 10/(x + 2) So, x = 22.

1070. A man can row 4.5 km/h in still water and he finds that it takes him twice as long to row up as to row down the river. The speed of the stream is

A. 2.5 km/h

B. 1.5 km/h

C. 2 km/h

D. 1.75 km/h

Explanation :

Let speed of stream be S and x be upstream speed.

Then for downstream, 4.5 + S = D

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And for upstream , 4.5 – S = U

So we get, D + U = 9

But, it takes him twice as long to row up as to row down the river.

3U = 9 ; U = 3. Thus, 4.5 – S = 3

S=1.5 kmph

1071. The average score of a cricketer for 13 matches is 42 runs. If his average score for the first 5 matches is 54, then what was his average score (in runs) for last 8 matches?

A. 37

B. 39

C. 34.5

D. 33.5

E. 37.5

Explanation :

Total Score = Average * Number of matches

Total score of 13 matches = 13 × 42 = 546

Total score of first 5 matches = 5 × 54 = 270

Therefore, total score of last 8 matches = 546 – 270 = 276

Average = 276/8 = 34.5

Hence the answer is option C

1072. Simple interest on a sum of money for 4 years at 7 p.c.p.a is Rs. 3584/-. What would be the compound interest (compounded annually) on the same amount of money for 2 years at 4p.c.p.a?

A. Rs. 1,162.32

B. Rs. 1,098.72

C. Rs. 992.38

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D. Rs. 1,231.76

E. Rs. 1,044.48

Explanation :

Let P be the sum

Therefore,

3584 = (P * 7 * 4) / 100 => P = 12800/-

CI = 12800(1 + (4/100))2 - 12800

=> 13844.48 - 12800 = 1044.48/-

Hence the answer is option E

1073. 6*136/8+132 / 628/16-26.25=?

A. 15

B. 24

C. 18

D. 12

E. 28

Explanation :

6*136/8+132 / 628/16-26.25

⇒ 234/13=18 Hence the answer is option C.

1074. (1097.63 + 2197.36 - 2607.24) ÷ 3.5 = ?

A. 211.5

B. 196.5

C. 209.5

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D. 192.5

E. 189.5

Explanation :

? = (1097.63 + 2197.36 - 2607.24) ÷ 3.5 = 687.75 ÷ 3.5

= 196.5

1075. A certain number of capsules were purchased for Rs. 216/-. 15 more capsules could have been purchased in the same amount if each capsule was cheaper by Rs. 10/-. What was the number of capsules purchased?

A. 6

B. 14

C. 8

D. 12

E. 9

Explanation :

Let x be the cost of each capsule and y be the no of capsules

Therefore, x = 216/y and x - 10 = 216/(y+15)

Putting the value of x from eq. 1 into eq. 2, we get

216/y - 216/(y+15) = 10

y2 +15y - 324 = 0

Solving for y, we get y = 12

1076. What will come in place of question mark (?)in the given question?

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4 6 34 ? 504 1234

A. 194

B. 160

C. 186

D. 156

E. 172

1077. A and B are two numbers. 6 times square of B is 540 more than the square of A. if the respective ratio between A and B is 3:2. What is the value of B?

A. 10

B. 12

C. 16

D. 8

E. 14

1078. A and B promise to do a work for Rs. 75. A alone can do it in 20 days and B in 30 days, with the help of C they are able to finish it in 8 days. How will A, B and C respectively distributes the wages?

A. Rs. 20, Rs. 30, Rs. 25

B. Rs. 25, Rs. 20, Rs. 30

C. Rs. 30, Rs. 25, Rs. 20

D. Rs. 30, Rs. 20, Rs. 25

E. None of these

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Explanation :

Everybody will get the wages according to their labour. A’s one day work = , A’s 8 days work = = ; B’s one day work = ;

B’s 8 days work = = , Remaining work = 1- - = ; C did the of work in 8 days.

wages are divided in the ratio of 2/5 : 4/15 :1/3 = 6 : 4 : 5 , A’s share = 6/15* 75= 30 Rs.

B’s share = 4/15* 75 = 20 Rs. ,C’s share = 5/15* 75 = 25 Rs.

1079. If 8 men or 12 women can do a piece of work in 25days, in how many days, can the work be done by 6 men and 11 women working together?

A. 12 days

B. 15 days

C. 9 days

D. 18 days

E. 10 days

Explanation :

8M = 12W s => 1M = W => ( 6M + 11W ) => D = 12W => 25 => ( 6 => W + 11W ) => D = 12W => 25 => 20 => D = 12 => 25 => D = 15 days

1080. A started a business by investing Rs. 25000. At the end of 4th month from the stat of the business B joined with Rs. 15000 and at the end of6th month from the start of the business, C joined with Rs. 20000. If the A’s share in profit at the end of year was Rs. 7,750, what was the total profit received?

A. Rs. 13,950

B. Rs. 13,810

C. Rs. 13,920

D. Rs. 12,780

E. Rs. 14,040

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Explanation :

A = 25000*12 , B = 15000*8, C = 20000*6

Ratio = A:B:C = 5:2:2. Let TP be the total profit.

Given, 5/9 * TP = 7750 => TP = 13950

1081. The respective ratio of radii of two right circular cylinders (A & B) is 3 : 2. The respective ratio of volumes of cylinders A and B is 9 : 7, then what are the heights of cylinders A and B?

A. 8 : 5

B. 4 : 7

C. 7 : 6

D. 5 : 4

E. 6 : 5

1082. Suri gave 25% of her monthly salary to her mother. From the remaining salary, she paid 15% towards rent and 25%, she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 42000. What was her monthly salary?

A. Rs. 50,000

B. Rs. 60,000

C. Rs. 65,000

D. Rs. 64,000

E. Rs. 72,000

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Explanation :

Let x be the total income

(75/100*60/100)x + 25/100x = 42000

Solving, x = 60000

1083. Nine students of a class contribute a certain sum. Seven of them give Rs. 5 each. The remaining two give Rs. 5 and Rs. 9 more than the average contribution of all the 9 students respectively. The average contribution of the class of 9 students is -

A. Rs. 10

B. Rs. 14

C. Rs. 7

D. Rs. 12

E. Rs 16

Explanation :

Let the average contribution of class = x (7*5) + (x + 5) + (x + 9) = 9x => 35 + 2x + 14 = 9x => 49 = 7x => x = 7.

1084. One-fourth of my marks in English is equal to one third of my marks in Hindi, The total number of marks secured by me in both the subjects is 140. The marks secured by me in English are...

A. 60

B. 80

C. 75

D. 85

E. None of these

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Explanation :

Let marks in English = x & Hindi = y.x/4 = y/3 Also x + y = 140. Solving the 2 equations we get x = 80.

1085. A boat takes a total time of twelve hours to travel 105 kms upstream and the same distance downstream. The speed of the boat in still water is six times of the speed of the current. What is the speed of the boat in still water? (In km/hr)

A. 12

B. 30

C. 18

D. 24

E. 36

Explanation :

Let ‘x’ be the speed of Boat in still water, and ‘y’ be the speed of current.

Then, according to the question,

Speed of the boat in still water = 6 speed of current

x = 6y

Also given that ,

105/(x+y) +105/(x-y) =12

105/7y +105/5y =12

12y=36

y=3

Therefore, x= 6×3=18

Speed of the boat in still water= 18kmph

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1086. At 60% of its usual speed, a train of length L metres crosses platform 240 metres long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in metres)?

A. 440

B. 425

C. 220

D. 480

E. 240

Explanation :

Let usual speed = S m/s.

According to the question,

60% of S= (L+240)/15

9S= L+240………… (i)

Also given that, S = L/6

L = 6S …. (ii)

From (i) & (ii)

9S= 6S+240

3S= 240

S=80 m/s

From (ii)

L= 6×80 =480 m

1087. P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of what Q has. If P, Q and R together have Rs. 240 then how much money does P alone have? (in Rs.)

A. 75

B. 60

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C. 120

D. 80

E. 90

Explanation :

Assume that P has 2x amount.

Therefore, Q = 3x amount (50% more than P)

And R = 3x × 1/3 = x

Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1

Thus, P alone have = (2/6) × 240 = Rs. 80

Most Asked Aptitude Questions Answers with Explanation For MNC and Competitive Exams Reviewed by jobs Tringle on October 05, 2020 Rating: 5