Pipes & Cisterns
8 questions · Hard
Pipes and cisterns is time and work with a twist: a filling pipe adds work and an emptying pipe takes it away.
💡 Quick tricks
- Filling pipe: +1/a of the tank per hour. Emptying pipe: −1/b per hour.
- Net rate with both open = 1/a − 1/b, so time = 1 ÷ net rate.
- If the net rate is negative, the tank empties instead of filling.
🎯 Try it yourself
Tap an answer. You'll see if it's right, and why. Easy ones come first.
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Q1Hard
Pipe A fills a tank in 10 hours, pipe B empties it in 14 hours. Both open: hours to fill?
Show answer
Answer: A. 35
💡 Net filling per hour = 1/10 − 1/14 = 1/35, so 35 hours.
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Q2Hard
Pipe A fills a tank in 8 hours, pipe B empties it in 16 hours. Both open: hours to fill?
Show answer
Answer: A. 16
💡 Net filling per hour = 1/8 − 1/16 = 1/16, so 16 hours.
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Q3Hard
A pipe fills a tank in 12 hours; a leak empties it in 15 hours. Hours to fill with both?
Show answer
Answer: A. 60
💡 Net filling per hour = 1/12 − 1/15 = 1/60, so 60 hours.
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Q4Hard
A pipe fills a tank in 12 hours; a leak empties it in 18 hours. Hours to fill with both?
Show answer
Answer: A. 36
💡 Net filling per hour = 1/12 − 1/18 = 1/36, so 36 hours.
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Q5Hard
Pipe A fills a tank in 4 hours, pipe B empties it in 8 hours. Both open: hours to fill?
Show answer
Answer: C. 8
💡 Net filling per hour = 1/4 − 1/8 = 1/8, so 8 hours.
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Q6Hard
A pipe fills a tank in 6 hours; a leak empties it in 24 hours. Hours to fill with both?
Show answer
Answer: A. 8
💡 Net filling per hour = 1/6 − 1/24 = 1/8, so 8 hours.
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Q7Hard
Pipe A fills a tank in 10 hours, pipe B empties it in 20 hours. Both open: hours to fill?
Show answer
Answer: B. 20
💡 Net filling per hour = 1/10 − 1/20 = 1/20, so 20 hours.
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Q8Hard
Pipe A fills a tank in 14 hours, pipe B empties it in 28 hours. Both open: hours to fill?
Show answer
Answer: B. 28
💡 Net filling per hour = 1/14 − 1/28 = 1/28, so 28 hours.
Your score
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