Pipes and Cisterns Exit
Quantitative aptitude

Pipes and Cisterns

Pipes are Time and Work with signs: filling pipes add, emptying pipes (and leaks) subtract.

Start with this

A pipe that fills a tank is a worker. A pipe that empties it is a worker doing negative work. That is the only difference from time and work.

Same method as time and work: total = LCM, inlets add, outlets subtract.

Inlets add, outlets subtract

Let the tank's capacity be the LCM of the times. Each filling pipe adds its units per hour, each emptying pipe takes away its units per hour.

If the net rate is negative, the tank never fills; it empties.

A fills in 12 hB fills in 15 hC empties in 20 h
Tank = 60 units. A +5, B +4, C -3: net +6 an hour, full in 10 h

Worked example

Pipes A and B fill a tank in 12 and 15 hours; C empties it in 20 hours. All three open together: how long to fill?

  1. Tank = LCM(12, 15, 20) = 60 units.
  2. A +5, B +4, C -3 per hour.
    Why: Emptying counts as negative.
  3. Net +6 per hour.
  4. 60 / 6 = 10 hours.

Answer: 10

A leak, and a pipe closed partway

A leak: a tank normally fills in 6 hours but takes 8 with a leak. Tank = 24 units: pipe +4, together +3, so the leak is -1 an hour and empties a full tank in 24 hours.

Pipe closed after some time: work out what was filled while it was open, then finish the rest with the pipes still running.

Worked example

A pipe fills a tank in 6 hours. Because of a leak it takes 8 hours. How long would the leak take to empty a full tank?

  1. Tank = LCM(6, 8) = 24.
  2. Pipe +4/h, with leak +3/h, so leak = -1/h.
    Why: The difference is the leak.
  3. 24 hours.

Answer: 24

Worked example

Pipes A and B fill a tank in 20 and 30 minutes. Both are opened, and A is closed after 5 minutes. How long does B take to finish?

  1. Tank 60. A 3/min, B 2/min.
  2. 5 minutes together: 25 units.
  3. Left 35, B alone: 17.5 minutes.

Answer: 17.5

Shortcut: Leak time

Use it when: 'Fills in 6 h, takes 8 h because of a leak'.

  1. Leak rate = 1/6 - 1/8 = 1/24.

Leak time: try it

As above. Leak alone empties in?

  1. 24 hours.

Answer: 24 hours

Your turn medium

A and B fill a tank in 20 and 30 min. Both are opened; after how many minutes must B be closed so the tank fills in exactly 15 min?

  1. A does 15/20 = 3/4.
  2. B must do 1/4 → 30/4 = 7.5 min.

Answer: 7.5 min

Your turn hard

A fills in 6 h, B in 8 h, opened alternately for 1 hour each, A first. Time to fill?

  1. 24 units. A 4, B 3 → 7 per 2 h.
  2. 6 h → 21. A needs 3 of 4 → 3/4 h.

Answer: 6 3/4 h

Your turn hard

Two pipes fill in 10 and 12 h; an outlet empties in 20 h. All open, but the outlet is closed after 2 h. Total time? (hours)

  1. First 2 h: 2 × (6 + 5 - 3)/60 = 16/60.
  2. Left 44/60 at 11/60 per hour = 4 h.
  3. Total 6 h.

Answer: 6 h

Your turn hard

Two inlets fill a tank in 12 and 15 min. With an outlet also open, it fills in 20 min. Outlet alone empties it in?

  1. 1/12 + 1/15 - 1/x = 1/20.
  2. 1/x = 9/60 - 3/60 = 1/10.

Answer: 10 min

Recap

Now practise

7 questions with full solutions.

Open practice Back to the lesson