Pipes And Cisterns Questions & Answers

Question 6

Easy

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the tree pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern?

A 90 minutes

B 100 minutes

C 110 minutes

D 120 minutes

Correct Answer: B

Explanation:

Let capacity = LCM(60, 75, 50) = 300 units. Rate of A = 300 / 60 = +5 units/min. Rate of B = 300 / 75 = +4 units/min. Combined rate of A + B + C = 300 / 50 = +6 units/min. Rate of C = Combined rate - (Rate A + Rate B) = 6 - (5 + 4) = 6 - 9 = -3 units/min. Time taken by C alone to empty the cistern = 300 / 3 = 100 minutes.

Question 7

Medium

Pipe P and Pipe Q can fill the tank in 40 hours and 25 hours respectively. If Pipe P and Pipe Q are opened alternatively starting with Pipe P, find the time taken to fill the tank.

A 30(2/5) hours

B 30(5/8) hours

C 31 hours

D 31(1/5) hours

Correct Answer: C

Explanation:

Let capacity = LCM(40, 25) = 200 units. Rate of P = 200 / 40 = 5 units/hour. Rate of Q = 200 / 25 = 8 units/hour. In a 2-hour cycle (P then Q): Work done = 5 + 8 = 13 units. In 15 cycles (30 hours): Work done = 15 × 13 = 195 units. Remaining capacity = 200 - 195 = 5 units. Hour 31 is P's turn with a rate of 5 units/hour. Time taken by P = 5 / 5 = 1 hour. Total time = 30 + 1 = 31 hours.

Question 8

Easy

A Cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?

A 6.5 hours

B 7 hours

C 7.2 hours

D 7.5 hours

Correct Answer: C

Explanation:

Let capacity = LCM(4, 9) = 36 units. Inflow rate = 36 / 4 = +9 units/hour. Outflow rate = -36 / 9 = -4 units/hour. Net filling rate = 9 - 4 = 5 units/hour. Time taken to fill = 36 / 5 = 7.2 hours.

Question 9

Easy

Pipe A and B are inlet pipes and pipe C is an outlet. Pipe A and B can fill the tank in 6 hours and 7.5 hours respectively and pipe C can empty the tank in 2 hours. If pipes A, B and C together are opened simultaneously, in how many hours the tank is filled/emptied completely?

A 5 hours to fill

B 5 hours to empty

C 6 hours to empty

D 4.5 hours to fill

Correct Answer: B

Explanation:

Let total tank capacity be LCM(6, 7.5, 2) = LCM(6, 15/2, 2) = 30 units. Rate of inlet A = +30 / 6 = +5 units/hour. Rate of inlet B = +30 / 7.5 = +4 units/hour. Rate of outlet C = -30 / 2 = -15 units/hour. Combined net rate = 5 + 4 - 15 = -6 units/hour. Since the net rate is negative, a full tank will be emptied. Time to empty the tank = Total capacity / Net rate = 30 / 6 = 5 hours to empty.

Question 10

Hard

An inlet pipe can fill a tank in 12 minutes. An outlet pipe can empty the same tank in 20 minutes. Mohit starts the inlet pipe at 10 a.m. At 10:05, the outlet pipe is opened accidently by Mohit. He realizes his mistake 8 minutes later and turns off the outlet pipe. At what time will the tank be completely filled?

A 10:14:24 a.m.

B 10:15:30 a.m.

C 10:16:48 a.m.

D 10:18:00 a.m.

Correct Answer: C

Explanation:

Let capacity = LCM(12, 20) = 60 units. Rate of inlet = 60 / 12 = +5 units/min. Rate of outlet = -60 / 20 = -3 units/min. From 10:00 to 10:05 (5 mins): Inlet alone fills: 5 × 5 = 25 units. From 10:05 to 10:13 (8 mins): Both pipes run: (5 - 3) × 8 = 2 × 8 = 16 units. Total filled by 10:13 am = 25 + 16 = 41 units. Remaining capacity = 60 - 41 = 19 units. At 10:13 am, outlet is turned off; only inlet runs at 5 units/min: Time needed = 19 / 5 = 3.8 minutes = 3 minutes 48 seconds. Time of completion = 10:13 am + 3 minutes 48 seconds = 10:16:48 am.

Pipes and Cistern Practice Questions