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

 

  • Correct Answer
    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 of the tank in a minute. A alone can fill of the tank in a minute. So, in a minute, B can fill . Or, B takes minutes to fill an entire tank.

To fill one-third the tank, B will take minutes. B is kept open for t - 10 minutes.

= 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)

Correct Answer: 24 minutes



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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.