**West Bengal P.C.S. Miscellaneous Services **

**Recruitment Exam., Solved Paper**

**(Arithmetic)**

**(Held on 9-3-2008)**

1. The diagonal of a square is 4√ 2 cm. The diagonal of another square whose area is double that of the first square is—

(A) 8 cm

(B) 8√2 cm

(C) 4√ 2 cm

(D) 16 cm

Ans : (A)

2. A train starts with the speed of 70 km/hr with its speed increasing every two hours by 10 km/hr. In how many hours will it cover 345 kms ?

(A) 2¼ hrs

(B) 4 hrs 5 mins

(C) 4½ hrs

(D) None of the above

Ans : (C)

3. How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ?

(A) 9•8 sec

(B) 12•1 sec

(C) 12•42 sec

(D) 14•3 sec

Ans : (B)

4. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water ?

(A) 40 mins

(B) 1 hr

(C) 1 hr 15 mins

(D) 1 hr 30 mins

Ans : (C)

5. The value of

is—

(A) 8 cm

(B) 8√2 cm

(C) 4√ 2 cm

(D) 16 cm

Ans : (A)

2. A train starts with the speed of 70 km/hr with its speed increasing every two hours by 10 km/hr. In how many hours will it cover 345 kms ?

(A) 2¼ hrs

(B) 4 hrs 5 mins

(C) 4½ hrs

(D) None of the above

Ans : (C)

3. How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ?

(A) 9•8 sec

(B) 12•1 sec

(C) 12•42 sec

(D) 14•3 sec

Ans : (B)

4. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water ?

(A) 40 mins

(B) 1 hr

(C) 1 hr 15 mins

(D) 1 hr 30 mins

Ans : (C)

5. The value of

is—

(A) 2

(B) 3/2

(C) 4/13

(D) 3 6/13

Ans : (A)

6. The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditure is 3 : 2. If at the end of each year, each saves Rs. 1600, then the income of A is—

(A) Rs. 3400

(B) Rs. 3600

(C) Rs. 4000

(D) Rs. 4400

Ans : (C)

7. Half of 1 per cent is equal to—

(A) 0•005

(B) 0•05

(C) 0•02

(D) 0•2

Ans : (A)

8. If 3/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it ?

(A) 40 sec

(B) 30 sec

(C) 36 sec

(D) 24 sec

Ans : (A)

9. In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth Rs. 8 per litre ?

(A) 1 : 2

(B) 2 : 1

(C) 2 : 3

(D) 3 : 2

Ans : (A)

10. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is—

(A) 214

(B) 476

(C) 954

(D) 1908

Ans : (A)

11. The difference between simple and compound interest @ 10% per annum on a sum of Rs. 1000 after 4 years is—

(A) Rs. 31

(B) Rs. 32•10

(C) Rs. 40•40

(D) Rs. 64•10

Ans : (D)

12. The maximum length of a pencil that can by kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, is—

(A) 2√13 cm

(B) 2√14 cm

(C) 2√26 cm

(D) 10√2 cm

Ans : (C)

13. What is the smallest number by which 3600 be divided to make it a perfect cube ?

(A) 9

(B) 450

(C) 50

(D) 300

Ans : (B)

14. At what time between 9 and 10 o’clock will the hands of a watch be together ?

(A) 45 min past 9

(B) 50 min past 9

(C) 49 1/11 min past 9

(D) 48 2/11 min past 9

Ans : (C)

15. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the number is reversed. The number is—

(A) 18

(B) 42

(C) 81

(D) 24

Ans : (D)

16. The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2 . The volume of the cuboid is—

(A) 24 cm3

(B) 48 cm3

(C) 64 cm3

(D) 120 cm3

Ans : (B)

17. In a school 10% of the boys are same in number as ¼ th of the girls. What is the ratio of boys to girls in the school ?

(A) 3 : 2

(B) 5 : 2

(C) 2 : 1

(D) 4 : 3

Ans : (B)

18. X got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price she bought. What was the labelled price ?

(A) Rs. 16,000

(B) Rs. 12,000

(C) Rs. 10,000

(D) None of the above

Ans : (C)

19. A vendor loses the selling price of 4 oranges on selling 36 oranges. Her loss per cent is—

(A) 10%

(B) 11 1/9 %

(C) 12 ½ %

(D) None of the above

Ans : (A)

20. In a camp, 95 men had provisions for 200 days. After 5 days, 30 men left the camp. For how many days will the remaining food last now ?

(A) 180

(B) 285

(C) 139 16/19

(D) 28•5

Ans : (B)

21. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds in terms of ratio of their speed.

(A) Dog’s speed : hare’s speed = 15 : 16

(B) Dog’s speed : hare’s speed = 16 : 15

(C) Dog’s speed : hare’s speed = 3 : 5

(D) Dog’s speed : hare’s speed = 5 : 3

Ans : (B)

22. The ratio of the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is—

(A) 70 km/hr

(B) 75 km/hr

(C) 84 km/hr

(D) 87•5 km/hr

Ans : (D)

23. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is—

(A)29years

(B) 19 years

(C) 49 years

(D) 39 years

Ans : (D)

24. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in—

(A) 6 hours

(B) 6 2/3 hours

(C) 7 hours

(D) 7 ½ hours

Ans : (C)

25. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)—

(A) 20, 35, 45

(B) 8, 20, 28

(C) 16, 28, 36

(D) 20, 36, 46

Ans : (C)

(B) 3/2

(C) 4/13

(D) 3 6/13

Ans : (A)

6. The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditure is 3 : 2. If at the end of each year, each saves Rs. 1600, then the income of A is—

(A) Rs. 3400

(B) Rs. 3600

(C) Rs. 4000

(D) Rs. 4400

Ans : (C)

7. Half of 1 per cent is equal to—

(A) 0•005

(B) 0•05

(C) 0•02

(D) 0•2

Ans : (A)

8. If 3/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it ?

(A) 40 sec

(B) 30 sec

(C) 36 sec

(D) 24 sec

Ans : (A)

9. In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth Rs. 8 per litre ?

(A) 1 : 2

(B) 2 : 1

(C) 2 : 3

(D) 3 : 2

Ans : (A)

10. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is—

(A) 214

(B) 476

(C) 954

(D) 1908

Ans : (A)

11. The difference between simple and compound interest @ 10% per annum on a sum of Rs. 1000 after 4 years is—

(A) Rs. 31

(B) Rs. 32•10

(C) Rs. 40•40

(D) Rs. 64•10

Ans : (D)

12. The maximum length of a pencil that can by kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, is—

(A) 2√13 cm

(B) 2√14 cm

(C) 2√26 cm

(D) 10√2 cm

Ans : (C)

13. What is the smallest number by which 3600 be divided to make it a perfect cube ?

(A) 9

(B) 450

(C) 50

(D) 300

Ans : (B)

14. At what time between 9 and 10 o’clock will the hands of a watch be together ?

(A) 45 min past 9

(B) 50 min past 9

(C) 49 1/11 min past 9

(D) 48 2/11 min past 9

Ans : (C)

15. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the number is reversed. The number is—

(A) 18

(B) 42

(C) 81

(D) 24

Ans : (D)

16. The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2 . The volume of the cuboid is—

(A) 24 cm3

(B) 48 cm3

(C) 64 cm3

(D) 120 cm3

Ans : (B)

17. In a school 10% of the boys are same in number as ¼ th of the girls. What is the ratio of boys to girls in the school ?

(A) 3 : 2

(B) 5 : 2

(C) 2 : 1

(D) 4 : 3

Ans : (B)

18. X got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price she bought. What was the labelled price ?

(A) Rs. 16,000

(B) Rs. 12,000

(C) Rs. 10,000

(D) None of the above

Ans : (C)

19. A vendor loses the selling price of 4 oranges on selling 36 oranges. Her loss per cent is—

(A) 10%

(B) 11 1/9 %

(C) 12 ½ %

(D) None of the above

Ans : (A)

20. In a camp, 95 men had provisions for 200 days. After 5 days, 30 men left the camp. For how many days will the remaining food last now ?

(A) 180

(B) 285

(C) 139 16/19

(D) 28•5

Ans : (B)

21. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds in terms of ratio of their speed.

(A) Dog’s speed : hare’s speed = 15 : 16

(B) Dog’s speed : hare’s speed = 16 : 15

(C) Dog’s speed : hare’s speed = 3 : 5

(D) Dog’s speed : hare’s speed = 5 : 3

Ans : (B)

22. The ratio of the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is—

(A) 70 km/hr

(B) 75 km/hr

(C) 84 km/hr

(D) 87•5 km/hr

Ans : (D)

23. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is—

(A)29years

(B) 19 years

(C) 49 years

(D) 39 years

Ans : (D)

24. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in—

(A) 6 hours

(B) 6 2/3 hours

(C) 7 hours

(D) 7 ½ hours

Ans : (C)

25. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)—

(A) 20, 35, 45

(B) 8, 20, 28

(C) 16, 28, 36

(D) 20, 36, 46

Ans : (C)

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