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Pipes and Cistern — Questions and Answers

Pipes and Cistern is Time and Work with a sign convention: inlet pipes add to the rate, outlet pipes and leaks subtract from it. Once you write every pipe as a fraction of the tank per hour, the arithmetic is identical to two people working together. The only genuinely new question types are "pipe closed after t hours" and "leak discovered after the tank was already filling".

21 solved questionsArithmetic AptitudeFree · no signup

Pipes and Cistern— Concepts, Formulas & Shortcuts

  • A pipe filling in n hours has rate 1/n of the tank per hour; an emptying pipe has rate −1/n.
  • Combined rate = sum of all inlet rates − sum of all outlet rates. Time = 1 / combined rate.
  • Use the LCM method: take the tank capacity as the LCM of the given times to avoid fractions.
  • If a full tank takes t₁ to fill without a leak and t₂ with it, the leak alone empties it in t₁t₂/(t₂ − t₁).
  • Pipe closed early: (time B runs)/B + (total time)/A = 1, then solve.
  • A negative combined rate means the tank never fills — a valid answer in some questions.

Pipes and Cistern Practice Questions with Answers

Attempt each question first, then open the explanation. All 21 questions below are free to read and require no signup.

  1. Q1.Pipe A fills a tank in 6 hours and pipe B in 4 hours. Together they fill it in:

    Easy
    • A2 hours
    • B2.4 hours
    • C2.5 hours
    • D3 hours
    +Show Answer & Explanation

    Answer: B. 2.4 hours

    Explanation: 1/6 + 1/4 = 5/12 per hour → 12/5 = 2.4 hours.

    Pipes and Cistern question 1 of 21

  2. Q2.A pipe fills a tank in 5 hours and another empties it in 10 hours. With both open the tank fills in:

    Easy
    • A5 hours
    • B8 hours
    • C10 hours
    • D15 hours
    +Show Answer & Explanation

    Answer: C. 10 hours

    Explanation: Net rate = 1/5 − 1/10 = 1/10 → 10 hours.

    Pipes and Cistern question 2 of 21

  3. Q3.Two pipes fill a tank in 20 and 30 minutes. Both are opened, but the second is closed after some time so the tank fills in 18 minutes. The second pipe was closed after:

    Difficult
    • A3 minutes
    • B5 minutes
    • C6 minutes
    • D8 minutes
    +Show Answer & Explanation

    Answer: A. 3 minutes

    Explanation: The first pipe runs 18 min → 18/20 = 0.9 of the tank. The second must supply 0.1 → t/30 = 0.1 → t = 3 minutes.

    Pipes and Cistern question 3 of 21

  4. Q4.Three pipes fill a tank in 10, 15 and 20 hours respectively. All three together fill it in:

    Moderate
    • A4 8/13 hours
    • B5 hours
    • C5 5/13 hours
    • D6 hours
    +Show Answer & Explanation

    Answer: A. 4 8/13 hours

    Explanation: 1/10 + 1/15 + 1/20 = 6/60 + 4/60 + 3/60 = 13/60 → 60/13 = 4 8/13 hours.

    Pipes and Cistern question 4 of 21

  5. Q5.A cistern is normally filled in 8 hours but takes 2 hours longer because of a leak. The leak alone would empty a full cistern in:

    Moderate
    • A20 hours
    • B30 hours
    • C40 hours
    • D48 hours
    +Show Answer & Explanation

    Answer: C. 40 hours

    Explanation: 1/8 − 1/L = 1/10 → 1/L = 1/8 − 1/10 = 1/40 → 40 hours.

    Pipes and Cistern question 5 of 21

  6. Q6.Two pipes fill a tank in 12 and 15 minutes while a waste pipe empties it in 10 minutes. With all three open the tank fills in:

    Moderate
    • A15 minutes
    • B18 minutes
    • C20 minutes
    • D24 minutes
    +Show Answer & Explanation

    Answer: C. 20 minutes

    Explanation: 1/12 + 1/15 − 1/10 = 5/60 + 4/60 − 6/60 = 3/60 = 1/20 → 20 minutes.

    Pipes and Cistern question 6 of 21

  7. Q7.Pipes A and B fill a tank in 15 and 20 hours. Both are opened together but A is closed after 4 hours. B alone then takes:

    Difficult
    • A8 hours
    • B9 1/3 hours
    • C10 2/3 hours
    • D12 hours
    +Show Answer & Explanation

    Answer: C. 10 2/3 hours

    Explanation: In 4 hours both fill 4(1/15 + 1/20) = 4 × 7/60 = 7/15. Remaining 8/15 at 1/20 per hour = 20 × 8/15 = 10 2/3 hours.

    Pipes and Cistern question 7 of 21

  8. Q8.A tap fills a tank in 6 hours. After half the tank is full, three more identical taps are opened. The total time to fill the tank is:

    Difficult
    • A3 h 15 min
    • B3 h 30 min
    • C3 h 45 min
    • D4 h
    +Show Answer & Explanation

    Answer: C. 3 h 45 min

    Explanation: The first half takes 3 hours. With 4 taps the rate is 4/6 = 2/3 per hour, so the second half takes 0.5 ÷ 2/3 = 0.75 h = 45 min. Total = 3 h 45 min.

    Pipes and Cistern question 8 of 21

  9. Q9.A pipe fills a tank in 10 hours and another in 15 hours. Together they fill it in:

    Easy
    • A5 hours
    • B6 hours
    • C7.5 hours
    • D12 hours
    +Show Answer & Explanation

    Answer: B. 6 hours

    Explanation: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 → 6 hours.

    Pipes and Cistern question 9 of 21

  10. Q10.A tank is filled by a pipe in 4 hours and emptied by another in 6 hours. With both open it fills in:

    Easy
    • A8 hours
    • B10 hours
    • C12 hours
    • DIt never fills
    +Show Answer & Explanation

    Answer: C. 12 hours

    Explanation: Net rate = 1/4 − 1/6 = 3/12 − 2/12 = 1/12 → 12 hours.

    Pipes and Cistern question 10 of 21

  11. Q11.Two pipes fill a tank in 6 and 8 hours, while a third empties it in 12 hours. With all three open the tank fills in:

    Moderate
    • A4 hours
    • B4.8 hours
    • C5 hours
    • D6 hours
    +Show Answer & Explanation

    Answer: B. 4.8 hours

    Explanation: 1/6 + 1/8 − 1/12 = 4/24 + 3/24 − 2/24 = 5/24 → 24/5 = 4.8 hours.

    Pipes and Cistern question 11 of 21

  12. Q12.A pipe can fill a tank in 20 minutes. Due to a leak it takes 25 minutes. The leak alone will empty the full tank in:

    Moderate
    • A50 minutes
    • B75 minutes
    • C100 minutes
    • D125 minutes
    +Show Answer & Explanation

    Answer: C. 100 minutes

    Explanation: 1/20 − 1/L = 1/25 → 1/L = 1/20 − 1/25 = 1/100 → 100 minutes.

    Pipes and Cistern question 12 of 21

  13. Q13.Two pipes A and B fill a tank in 12 and 18 minutes. If both are opened together, the tank fills in:

    Easy
    • A6 minutes
    • B7.2 minutes
    • C8 minutes
    • D9 minutes
    +Show Answer & Explanation

    Answer: B. 7.2 minutes

    Explanation: 1/12 + 1/18 = 3/36 + 2/36 = 5/36 → 36/5 = 7.2 minutes.

    Pipes and Cistern question 13 of 21

  14. Q14.A cistern has two inlets filling it in 8 and 12 hours. If both run for 3 hours, the fraction of the tank filled is:

    Moderate
    • A3/8
    • B5/8
    • C1/2
    • D2/3
    +Show Answer & Explanation

    Answer: B. 5/8

    Explanation: Combined rate = 1/8 + 1/12 = 5/24 per hour → in 3 hours, 15/24 = 5/8.

    Pipes and Cistern question 14 of 21

  15. Q15.A tap fills a tank in 30 minutes and a second in 45 minutes. If the first runs alone for 10 minutes and then both run together, the total time taken is:

    Difficult
    • A20 minutes
    • B22 minutes
    • C24 minutes
    • D26 minutes
    +Show Answer & Explanation

    Answer: B. 22 minutes

    Explanation: In 10 minutes the first tap fills 10/30 = 1/3. The remaining 2/3 at a combined rate of 1/30 + 1/45 = 5/90 = 1/18 per minute takes 12 minutes. Total = 10 + 12 = 22 minutes.

    Pipes and Cistern question 15 of 21

  16. Q16.A pipe fills a tank in 8 hours and another in 8 hours. Together they take:

    Easy
    • A2 hours
    • B4 hours
    • C6 hours
    • D16 hours
    +Show Answer & Explanation

    Answer: B. 4 hours

    Explanation: 1/8 + 1/8 = 1/4 → 4 hours.

    Pipes and Cistern question 16 of 21

  17. Q17.A tap fills a tank in 12 minutes and a leak empties it in 24 minutes. With both open the tank fills in:

    Moderate
    • A18 minutes
    • B20 minutes
    • C24 minutes
    • D36 minutes
    +Show Answer & Explanation

    Answer: C. 24 minutes

    Explanation: Net rate = 1/12 − 1/24 = 1/24 → 24 minutes.

    Pipes and Cistern question 17 of 21

  18. Q18.Three pipes fill a tank in 6, 12 and 12 hours. Together they take:

    Moderate
    • A2 hours
    • B3 hours
    • C4 hours
    • D5 hours
    +Show Answer & Explanation

    Answer: B. 3 hours

    Explanation: 1/6 + 1/12 + 1/12 = 2/12 + 1/12 + 1/12 = 4/12 = 1/3 → 3 hours.

    Pipes and Cistern question 18 of 21

  19. Q19.A pipe fills a cistern in 15 minutes. In 5 minutes it fills what fraction?

    Easy
    • A1/5
    • B1/4
    • C1/3
    • D1/2
    +Show Answer & Explanation

    Answer: C. 1/3

    Explanation: 5/15 = 1/3 of the cistern.

    Pipes and Cistern question 19 of 21

  20. Q20.Two pipes fill a tank in 10 and 40 minutes. Together they take:

    Moderate
    • A6 minutes
    • B8 minutes
    • C12 minutes
    • D25 minutes
    +Show Answer & Explanation

    Answer: B. 8 minutes

    Explanation: 1/10 + 1/40 = 4/40 + 1/40 = 5/40 = 1/8 → 8 minutes.

    Pipes and Cistern question 20 of 21

  21. Q21.A cistern fills in 6 hours but a leak makes it take 9 hours. The leak alone empties it in:

    Difficult
    • A12 hours
    • B15 hours
    • C18 hours
    • D24 hours
    +Show Answer & Explanation

    Answer: C. 18 hours

    Explanation: 1/6 − 1/L = 1/9 → 1/L = 1/6 − 1/9 = 1/18 → 18 hours.

    Pipes and Cistern question 21 of 21

Pipes and Cistern — Frequently Asked Questions

How do I handle a leak in a cistern problem?+

Treat it as a negative rate. If the inlet fills in 8 hours but with the leak it takes 10, then 1/8 − 1/L = 1/10 gives 1/L = 1/40, so the leak empties a full tank in 40 hours.

What if one pipe is closed before the tank is full?+

Write the total work as 1: the pipe that runs the whole time contributes (total time)/its time, and the pipe closed early contributes (its running time)/its time. Set the sum equal to 1.

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