Pipes And Cisterns Questions & Answers

Question 11

Easy

Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off,so that the cistern be fill in 24 minutes?

A 12 minutes

B 14 minutes

C 16 minutes

D 18 minutes

Correct Answer: C

Explanation:

Let capacity = LCM(36, 48) = 144 units. Rate of P = 144 / 36 = 4 units/min. Rate of Q = 144 / 48 = 3 units/min. The cistern is filled in 24 minutes, meaning pipe P runs for the full 24 minutes. Work done by P in 24 minutes = 4 × 24 = 96 units. Work to be completed by Q = 144 - 96 = 48 units. Time for which Q must remain open = 48 / 3 = 16 minutes.

Question 12

Medium

Pipes A, B and C can fill the tank in 36 minutes, 48 minutes and 72 minutes respectively. Both pipes A and B opened together and after x minutes, pipe C also opened and the remaining tank was filled by pipes A, B and C together in 9 minutes. Find the value of x?

A 8 minutes

B 9 minutes

C 10 minutes

D 12 minutes

Correct Answer: B

Explanation:

Let capacity = LCM(36, 48, 72) = 144 units. Rate of A = 144 / 36 = 4 units/min. Rate of B = 144 / 48 = 3 units/min. Rate of C = 144 / 72 = 2 units/min. Combined rate of A, B, and C = 4 + 3 + 2 = 9 units/min. In the last 9 minutes, A, B, and C fill: 9 × 9 = 81 units. Work filled by A and B in the first x minutes = 144 - 81 = 63 units. Rate of (A + B) = 4 + 3 = 7 units/min. Therefore, x = 63 / 7 = 9 minutes.

Question 13

Hard

Four pipes P, Q, R and S can fill a cistern in 25, 20, 50 and 40 hours respectively. The pipe Q was opened at 7 pm, P at 9 pm, S at 10 pm and R at 11 pm. When will the cistern be full?

A Next day 3:45 am

B Next day 4:09 am

C Next day 4:30 am

D Next day 5:00 am

Correct Answer: B

Explanation:

Let cistern capacity = LCM(25, 20, 50, 40) = 200 units. Rate of P = 200 / 25 = 8 units/hr. Rate of Q = 200 / 20 = 10 units/hr. Rate of R = 200 / 50 = 4 units/hr. Rate of S = 200 / 40 = 5 units/hr. From 7 pm to 11 pm (4 hours): Q runs: 10 × 4 = 40 units. From 9 pm to 11 pm (2 hours): P runs: 8 × 2 = 16 units. From 10 pm to 11 pm (1 hour): S runs: 5 × 1 = 5 units. Total water filled by 11 pm = 40 + 16 + 5 = 61 units. Remaining capacity at 11 pm = 200 - 61 = 139 units. At 11 pm, all four pipes (P + Q + R + S) operate together: Combined rate = 8 + 10 + 4 + 5 = 27 units/hr. Additional time taken = 139 / 27 hours = 5 hours + (4/27) × 60 mins = 5 hours 8.88 mins ≈ 5 hours 9 minutes. Time of completion = 11:00 pm + 5 hours 9 minutes = 4:09 am next day.

Question 14

Easy

An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3(1/2) hours to fill the tank. If the tank is full, how much time will the leak take to empty it?

A 18 hours

B 20 hours

C 21 hours

D 24 hours

Correct Answer: C

Explanation:

Normal filling rate = 1/3 per hour. Net rate with leak = 1 / (7/2) = 2/7 per hour. Leak rate = 1/3 - 2/7 = (7 - 6)/21 = 1/21 per hour. Time taken by leak alone = 21 hours.

Question 15

Medium

The cistern has inlet pipes P and Q and an outlet pipe R. Pipes P, Q can fill the cistern alone in 15 hours and 18 hours respectively and Pipe R can empty the cistern in 27 hours. In the first 5 hours, P and Q are opened together and then for the next 12 hours, pipe Q and R are opened together. How many hours Q alone can fill the remaining tank?

A 2 hours

B 3 hours

C 4 hours

D 2.5 hours

Correct Answer: B

Explanation:

Let total cistern capacity = LCM(15, 18, 27) = 270 units. Rate of P = 270 / 15 = +18 units/hour. Rate of Q = 270 / 18 = +15 units/hour. Rate of R = -270 / 27 = -10 units/hour. In first 5 hours (P + Q): (18 + 15) × 5 = 33 × 5 = 165 units. In next 12 hours (Q + R): (15 - 10) × 12 = 5 × 12 = 60 units. Total filled so far = 165 + 60 = 225 units. Remaining volume = 270 - 225 = 45 units. Time taken by Q alone = 45 / 15 = 3 hours.

Pipes and Cistern Practice Questions