Solve these pipes and cisterns problems to ace math part

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions, answers and explanations on the Pipes and Cisterns topic.

1. There are two pipes which are functioning simultaneously to fill a tank in 12 hours. If one pipe fills the tank 10 hours faster than the other, then how many hours second pipe will take to fill the tank?
a) 30 hours b) 35 hours c) 40 hours d) 42 hours
Ans: a

Explanation:
Let’s suppose tank got filled by first pipe in X hours.

So, second pipe will fill the tank in x 10 hours.

So, 1/x 1/(x 10) = 1/12

X = 20 hours
Second pipe will take x 10 hours = 30 hours.
2. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then, the slower pipe alone will be able to fill the tank in?

a) 144 min b) 140 min c) 136 min d) 132 min

Ans: a

Explanation:
Let the slower pipe alone fill the tank in x minutes

Then, faster pipe will fill in x/3 minutes.

Part filled by slower pipe in 1 minute = 1/x

Part filled by faster pipe in 1 minute = 3/x

Part filled by both in 1 minute = 1/x 3/x = 1/36
→ 4/x = 1/36 → x = 4×36 = 144 minutes.

3. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
a) 8 min 15 sec b) 7 min 15 sec
c) 6 min 15 sec d) 5 min 15 sec
Ans: a

Explanation:
Part filled in 3 minutes = 3(1/12 1/15) = 3× 9/60 = 9/20

Remaining part = 1- 9/20= 11/20
So, 1/15: 11/20 = 1:x

X= 11/20 × 15 = 8.25 minutes
So, it will take further 8 minutes 15 seconds to fill the bucket.
4. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

a) 3 hours 15 minutes b) 3 hours 45 minutes
c) 4 hours d) 4 hours 15 minutes
Ans: b

Explanation:
Time taken by one tap to fill half of the tank = 3 hours

Part filled by the four taps in 1 hour = 1/6×4= 2/3

Remaining part = 1- 1/2 = 1/2
X = (1/2) × 1 × (3/2) = 3/4 hours i.e., 45 minutes

So, total time taken = 3 hours 45 minutes.

5. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is?

a) 10 b) 12 c) 14 d) 16

Ans: c

Explanation:

Part filled by (A B C) in 2 hours = 2/6 = 1/3
Let be the Part filled by A and B in 7 hours = 2/3

Part filled by A and B in 1 hour = 2/(3×7) = 2/21
So, A and B together can fill the tank in 21/2 hours

So, (c×21/2)/(c 21/2) = 6 =>; 21c/(2c 21)=6

9c = 21×6 =>; C= 14.

By Banda Ravipal Reddy

Director, SIGMA

Sai Institute of General Mental Ability

Hyderabad