Pipe & Work Question Answers

Pipes and Cisterns - Quant/Math - CAT 2008

Question 4 the day: May 27, 2002

The question for the day is from the topic Pipes and Cisterns. The problems from the topic Pipes and Cisterns and Work and Time are very similar in nature. So, if you understand the nature of one of these types, you will be able to attempt the other quite comfortably.

There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

(1)

6

(2)

8

(3)

7

(4)

5

Correct Answer - (3)

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Solution

Let there be �n� fill pipes attached to the tank.
Therefore, there will be 12 - n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th of the tank in an hour.
Hence, n fill pipes will fill n*1/8 = n/8 th of the tank in an hour.
Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain 1/6 th of the tank in an hour.
Hence, 12 - n drain pipes will drain(12-n) / 6  =  12-n  /  of the tank in an hour.
When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow. Therefore, in an hour 1/24 thof the tank gets filled.
Hence,n/8 - 12 - n/6 = 1/24.
i.e.3n - 4(12-n)  /  24  =  1/24  or 7n - 48 = 1 => 7n = 49 or n = 7.