Quantitative Aptitude

Pipes and Cisterns: Practice Questions with Answers

14 practice questions on Pipes and Cisterns, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

Read the lesson on this topic →

1. Q.1

   Pipe A can fill a tank in 12 hours, and Pipe B can fill it in 15 hours. Pipe A is opened first, and Pipe B joins 4 hours later. Find the total time taken to fill the tank.

   Show answer

   Answer: 76/9 hours ≈ 8.44 hours

   Solution:

   1. In the first 4 hours, only A works: it fills 4 × (1/12) = 1/3 of the tank. Remaining = 2/3.
   2. Once both are open, combined rate = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20.
   3. Time to fill the remaining 2/3 at this rate = (2/3) ÷ (3/20) = (2/3) × (20/3) = 40/9 hours.
   4. Total time = 4 + 40/9 = 36/9 + 40/9 = 76/9 ≈ 8.44 hours (8 hours and about 27 minutes).

   Report this question

2. Q.2

   Pipe A can fill a tank in 6 hours, and Pipe B can fill the same tank in 8 hours. If both pipes are opened together, how long will it take to fill the tank?

   Show answer

   Answer: 24/7 hours = 3 3/7 hours

   Solution:

   1. Rate A = 1/6, Rate B = 1/8. Combined rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24.
   2. Time = 1 ÷ (7/24) = 24/7 = 3 3/7 hours.

   Report this question

3. Q.3

   Two pipes can fill a tank in 12 hours and 15 hours respectively. A third outlet pipe can empty the full tank in 20 hours. If all three are opened together, how long will it take to fill the empty tank?

   Show answer

   Answer: 10 hours

   Solution:

   1. Rates: 1/12, 1/15, and −1/20. Using 60 as a common denominator: 5/60 + 4/60 − 3/60 = 6/60 = 1/10.
   2. Time = 1 ÷ (1/10) = 10 hours.

   Report this question

4. Q.4

   Pipe A can fill a tank in 6 hours. When pipe A and an outlet pipe B are opened together, the tank fills in 10 hours. Find the time pipe B alone would take to empty the full tank.

   Show answer

   Answer: 15 hours

   Solution:

   1. Set up the combined-rate equation with B's rate as the unknown: 1/6 − 1/y = 1/10.
   2. 1/y = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15.
   3. So y = 15 hours.

   Report this question

5. Q.5

   A tank can be filled by Pipe A in 4 hours. Pipe A is twice as fast as Pipe B. If both pipes work together, how long will they take to fill the tank?

   Show answer

   Answer: 8/3 hours = 2 2/3 hours

   Solution:

   1. Pipe A’s rate = 1/4. "A is twice as fast as B" means A’s rate is double B’s rate, so B’s rate = (1/4) ÷ 2 = 1/8 (B alone would take 8 hours).
   2. Combined rate = 1/4 + 1/8 = 2/8 + 1/8 = 3/8.
   3. Time = 1 ÷ (3/8) = 8/3 = 2 2/3 hours.

   Report this question

6. Q.6

   Pipe A can fill a tank in 5 hours, while Pipe B (an outlet) can empty the full tank in 10 hours. If both pipes are opened together, how long will it take to fill the empty tank?

   Show answer

   Answer: 10 hours

   Solution:

   1. Rate A = 1/5, Rate B = −1/10. Combined rate = 1/5 − 1/10 = 2/10 − 1/10 = 1/10.
   2. Time = 1 ÷ (1/10) = 10 hours.

   Report this question

7. Q.7

   Pipes A and B can fill a tank in 15 and 20 hours respectively. Both are opened together, but after 4 hours, Pipe A is closed. Find the total time taken to fill the tank.

   Show answer

   Answer: 44/3 hours ≈ 14.67 hours

   Solution:

   1. Combined rate for the first 4 hours = 1/15 + 1/20 = 4/60 + 3/60 = 7/60.
   2. Filled in 4 hours = 4 × 7/60 = 28/60 = 7/15. Remaining = 8/15.
   3. Only B works after this, at rate 1/20. Time for the rest = (8/15) ÷ (1/20) = (8/15) × 20 = 160/15 = 32/3 hours ≈ 10.67 hours.
   4. Total time = 4 + 32/3 = 12/3 + 32/3 = 44/3 ≈ 14.67 hours (about 14 hours 40 minutes).

   Report this question

8. Q.8

   Pipe A can fill a tank in 6 hours, while Pipe B (an outlet) can empty the full tank in 9 hours. If both are opened together, how long will it take to fill the empty tank?

   Show answer

   Answer: 18 hours. Combined rate = 1/6 − 1/9 = 1/18.

   Report this question

9. Q.9

   Pipe A can fill a tank in 10 hours, and Pipe B can fill the same tank in 15 hours. If both are opened together, how long will it take to fill the tank?

   Show answer

   Answer: 6 hours. Combined rate = 1/10 + 1/15 = 1/6.

   Report this question

10. Q.10

    Pipes A and B can fill a tank in 12 and 24 hours respectively. Both are opened together, but after 4 hours, Pipe A is closed. Find the total time to fill the tank.

    Show answer

    Answer: 16 hours. First 4 hrs (combined rate 1/8) fill 1/2; remaining 1/2 at B's rate 1/24 takes 12 hrs; total 4+12.

    Report this question

11. Q.11

    A tank is filled by Pipe A in 9 hours. Pipe A is 1.5 times as fast as Pipe B. If both work together, how long will they take to fill the tank?

    Show answer

    Answer: 5.4 hours. B's rate = (1/9)/1.5 = 2/27; combined = 3/27+2/27 = 5/27; time = 27/5.

    Report this question

12. Q.12

    Pipe A can fill a tank in 12 hours, and Pipe B in 18 hours. Pipe A is opened first, and Pipe B joins 3 hours later. Find the total time to fill the tank.

    Show answer

    Answer: 8.4 hours. First 3 hrs fill 1/4; remaining 3/4 at combined rate 5/36 takes 5.4 hrs; total 3+5.4.

    Report this question

13. Q.13

    Pipe A can fill a tank in 8 hours. When pipe A and an outlet pipe B are opened together, the tank fills in 24 hours. Find the time pipe B alone would take to empty the tank.

    Show answer

    Answer: 12 hours. 1/y = 1/8 − 1/24 = 1/12.

    Report this question

14. Q.14

    A tank can be filled by Pipe A in 12 hours. Pipe A is 3 times as fast as Pipe B. If both work together, how long will they take to fill the tank?

    Show answer

    Answer: 9 hours. B's rate = 1/36; combined = 1/12 + 1/36 = 1/9.

    Report this question

Practise this topic →