# CAT Practice : Pipes cisterns, Work time

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If you had three pipes and wanted to keep them open for different stretches of time, no one can stop you from doing that.

## Three Pipes

Q.2: Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will C alone take to fill the tank?
1. 18
2. 36
3. 27
4. 24

Choice D. 24

## Detailed Solution

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.

A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.

A and B together can fill ${1 \over t}$ of the tank in a minute. A alone can fill ${1 \over 3t}$ of the tank in a minute. So, in a minute, B can fill ${1 \over t} {-} {1 \over 3t} {=} {2 \over 3t}$. Or, B takes ${3t \over 2}$ minutes to fill an entire tank.

To fill one-third the tank, B will take ${t \over 2}$ minutes. B is kept open for t - 10 minutes.

${t \over 2}$ = t - 10, t = 20 minutes.

A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.

C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes. Choice (D)

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## More questions from Pipes Cisterns, Work Time

Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.