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Pipes and Cisterns: Inlets, Outlets, Leaks and Waste Pipes

Rates per hour • Inlet minus outlet • Leak time • Pipes closed midway • Capacity in litres

SSC Banking Railway 📅 Last updated: 2026-10-20

Pipes and cisterns questions look different from time and work, but the method is the same. A pipe that fills a tank in 12 hours fills 1/12 of the tank every hour. That hourly fraction is its rate, and rates are what you add.

The new element is direction. An inlet adds water, so its rate is positive. An outlet, a waste pipe or a leak removes water, so its rate is negative. Add all the rates, with signs, to get the net rate. The time to fill or empty the tank is the reciprocal of that net rate.

Net rate = sum of inlet rates − sum of outlet rates; time = 1 ÷ net rate. A negative net rate means the tank is emptying.

Worked example 1: two inlets

Pipe A fills a tank in 12 hours and pipe B in 15 hours. Together they fill 1/12 + 1/15 = 9/60 = 3/20 of the tank each hour. Time = 20/3 hours = 400 minutes, that is 6 hours 40 minutes.

The LCM method avoids fractions. Take the tank as 60 units, the LCM of 12 and 15. A then fills 5 units an hour and B fills 4, so together they fill 9 units an hour and need 60/9 hours. You get the same answer with whole numbers throughout, which is faster under time pressure.

Worked example 2: an inlet against an outlet

An inlet fills a tank in 10 hours and an outlet empties it in 15 hours. Net rate = 1/10 − 1/15 = 1/30, so with both open the tank fills in 30 hours. In LCM units: tank = 30, inlet +3 an hour, outlet −2 an hour, net +1 an hour.

A leak is an outlet you cannot see. Questions usually give the normal fill time (x) and the slower fill time with the leak (y). The leak's rate is the difference of the two rates, 1/x − 1/y, so the leak alone empties a full tank in:

Leak time = xy ÷ (y − x)

Worked example 3: finding the leak

A pipe fills a tank in 6 hours, but with a leak the tank takes 8 hours. Leak time = (6 × 8) ÷ (8 − 6) = 24 hours. Check: 1/6 − 1/8 = 1/24.

With three or more pipes, add every inlet rate and subtract every outlet rate in a single step.

Worked example 4: two inlets and an outlet

A fills in 20 minutes, B in 30 minutes and C empties in 15 minutes. Net rate = 1/20 + 1/30 − 1/15 = (3 + 2 − 4)/60 = 1/60. The tank fills in 60 minutes.

When a pipe is closed partway through, split the job into stages. Find what was filled while all the pipes ran, subtract it from one whole tank, then divide the remainder by the rate of the pipes still open.

Worked example 5: closing a pipe after 4 hours

A fills in 12 hours and B in 18 hours. Both run for 4 hours and fill 4 × (1/12 + 1/18) = 5/9 of the tank. A fills the remaining 4/9 in (4/9) × 12 = 16/3 hours. Total = 4 + 16/3 = 28/3 hours = 560 minutes, or 9 hours 20 minutes.

When a waste pipe removes a fixed number of litres per minute, call the capacity C and write each pipe's rate in litres: C/20 litres a minute for a 20-minute pipe, and so on. Then set the combined rate equal to C divided by the combined time.

Worked example 6: capacity from a waste pipe

Two pipes fill a tank in 20 and 24 minutes. A waste pipe removes 3 litres a minute. With all three open, the tank fills in 15 minutes. So C/20 + C/24 − 3 = C/15, which gives C × (6 + 5 − 8)/120 = 3 and C = 120 litres.

  • ✘ Adding or averaging times instead of rates.
  • ✘ Forgetting the minus sign for an outlet or a leak.
  • ✘ Applying a pipe's rate for the whole job when it was closed partway through.
  • ✘ Mixing hours and minutes. Convert everything to one unit before adding.
SituationTime
Inlets x and y togetherxy ÷ (x + y)
Inlet x, outlet y (y > x)xy ÷ (y − x) to fill
Fill time x becomes y because of a leakleak empties in xy ÷ (y − x)
Any number of pipes1 ÷ (sum of signed rates)

For the full LCM technique, see time and work by the LCM method. Other formulas are collected in the Quant cheat code.

Q1. Pipe A fills a tank in 10 hours and pipe B in 15 hours. Working together, how long do they take? easy

✅ Answer: (a) 6 hours

💡 Explanation: Rates add: 1/10 + 1/15 = 5/30 = 1/6 of the tank per hour, so the tank fills in 6 hours. Averaging the times (12.5) is wrong.

Q2. An inlet fills a tank in 8 hours and an outlet empties it in 12 hours. If both are opened on an empty tank, when is it full? easy

✅ Answer: (c) 24 hours

💡 Explanation: Net rate = 1/8 − 1/12 = 1/24 of the tank per hour, so the tank fills in 24 hours.

Q3. A pipe fills a tank in 4 hours, but because of a leak it takes 5 hours. How long would the leak take to empty a full tank? medium

✅ Answer: (b) 20 hours

💡 Explanation: Leak rate = 1/4 − 1/5 = 1/20 per hour, so it empties the tank in 20 hours. The shortcut xy/(y − x) = 20/1 gives the same.

Q4. Pipes A and B fill a cistern in 12 and 15 minutes, and pipe C empties it in 20 minutes. If all three are opened together, how long does it take to fill? medium

✅ Answer: (d) 10 minutes

💡 Explanation: Net rate = 1/12 + 1/15 − 1/20 = (5 + 4 − 3)/60 = 1/10 per minute, so the cistern fills in 10 minutes.

Q5. Pipes A and B fill a tank in 30 and 20 minutes. Both are opened, and A is closed after 6 minutes. How long does the tank take to fill in total? medium

✅ Answer: (a) 16 minutes

💡 Explanation: In 6 minutes both fill 6 × (1/30 + 1/20) = 1/2 of the tank. B fills the other half in 10 minutes, so the total is 16 minutes.

Q6. Two pipes fill a tank in 12 and 16 minutes. A waste pipe removes 2 litres a minute. With all three open, the tank fills in 8 minutes. What is its capacity? hard

✅ Answer: (c) 96 litres

💡 Explanation: If the capacity is C, then C/12 + C/16 − 2 = C/8. This gives C × (1/48) = 2, so C = 96 litres.

Is pipes and cisterns the same as time and work?

Yes, in method. Filling a tank is the work, each pipe is a worker, and an outlet or leak is a worker who undoes work. The only new idea is the negative sign for outlets, so the time and work LCM method applies directly.

How do I handle a tank that starts half full?

Multiply the time for a full tank by the fraction that still has to be filled or emptied. If the net rate fills a full tank in 30 hours and the tank is already half full, the rest takes 15 hours.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 12 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveen on 2026-10-20 against the sources listed above.

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