West Bengal
P.C.S. Miscellaneous Services
Recruitment
Exam Solved Paper
Arithmetic
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) 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)
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