Pipes and Cistern – Formulas, Tricks, Aptitude Questions and Solved Examples with Explanation

Formulas and Quick Tricks for Pipes and Cistern

1. If a pipe can fill a tank in x hours, then part of tank filled in one hour = 1/x
2. If a pipe can empty a full tank in y hours, then part emptied in one hour = 1/y
3. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then on opening both the pipes:
   • the net part filled in 1 hour = (1/x-1/y), if y > x
   • the net part emptied in 1 hour = (1/y-1/x), if x > y

Questions and Solved Examples on Pipes and Cistern

Q.1: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the 3 pipes are opened at the same time?
A. 7 1/7 mins.
B. 15 1/7 mins.
C. 17 1/7 mins.
D. 19 1/7 mins.
Answer: B. 17 1/7 mins
Explanation: 1/20 + 1/30 – 1/40 = 7/120
=>120/7 = 17 1/7

Q.2: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
A. 7 mins.
B. 9 mins.
C. 13 mins.
D. 23 mins.
Answer: B. 9 mins
Explanation: 1/10 + 1/15 – 1/x = 1/18
x = 9


Q.3: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
A. 16 hrs
B. 20 hrs
C. 25 hrs
D. 40 hrs
Answer: D. 40 hrs
Explanation: 1/8 – 1/x = 1/10
x = 40

Q.4: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A. 9 mins.
B. 10 mins.
C. 11 mins.
D. 12 mins.
Answer: B. 10 mins
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 – 1/45 = (5 + 6 – 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes

Q.5: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
A. 19 mins.
B. 20 mins.
C. 21 mins.
D. 22 mins.
Answer: C. 21 mins
Explanation: Let the pipe B be closed after x minutes.
30/16 – x/24 = 1 => x/24 = 30/16 – 1 = 14/16
=> x = 14/16 * 24 = 21

Q.6: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
A. 5/11
B. 6/11
C. 7/11
D. 8/11
Answer: B. 6/11
Explanation: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11

Q.7: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
A. 5/11
B. 6/11
C. 7/11
D. 8/11
Answer: B. 6/11
Explanation: Part filled by (A + B + C) in 3 minutes = 3 (1 / 30 + 1 / 20 + 1 / 10) = (3 * 11 / 60) = 11 / 20
Part filled by C in 3 minutes = 3 / 10
Therefore, required ratio = (3 / 10 * 20 / 11) = 6/11

Q.8: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A. 1 13/17 hrs
B. 2 8/11 hrs
C. 3 9/17 hrs
D. 4 1/2 hrs
Answer: C. 3 9/17 hrs
Explanation: Net part filled in 1 hour (1 / 5 + 1 / 6 – 1 / 12) = 17 / 60
Therefore, the tank will be full in 60 / 17 hours i.e., 3 9/17 hrs


Q.9: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in:
A. 10 hrs
B. 12 hrs
C. 14 hrs
D. 16 hrs
Answer: C. 14 hrs
Explanation: Work done by the leak in 1 hour = (1/2 – 3/7) = 1/14
Leak will empty the tank in 14 hrs

Q.10: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A. 6 mins.
B. 9 mins.
C. 12 mins.
D. 15 mins.
Answer: B. 9 mins.
Explanation: Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 – x) min. = 1
Therefore, x(2/75 + 1/45) + (30 – x) = 2/75 = 1
=> 11x/225 + (60 – 2x)/75 = 1
=> 11x + 180 – 6x = 225
=> x = 9