Pipe & Work Question Answers

Pipes and Cisterns - Quant/Math - CAT 2008

Question 4 the day: April 8, 2002

A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?

(1)

2

(2)

4

(3)

6

(4)

5

Correct Answer - (2)

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Solution:

Let the number of fill pipes be �n'. Therefore, there will be 8-n, waste pipes.
Each of the fill pipes can fill the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8^th of the tank in an hour.
Hence, n fill pipes will fill n/8^th of the tank in an hour.

Similarly, each of the waste pipes will drain the full tank in 6 hours. That is, each of the waste pipes will drain 1/6^th of the tank in an hour.
Therefore, (8-n) waste pipes will drain ((8-n)/6)^th of the tank in an hour.

Between the fill pipes and the waste pipes, they drain the tank in 6 hours. That is, when all 8 of them are opened, 1/6^th of the tank gets drained in an hour.

(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1 hour)
 = 1/6^th capacity of the tank drained in 1 hour.

n/8  -  8-n / 6  =  -1/6  =>  6n-64+8n / 48  =  -1/6  => 14n-64= -8 or 14n = 56 or n=4   

Note: In problems pertaining to Pipes and Cisterns, as a general rule find out the amount of the tank that gets filled or drained by each of the pipes in unit time (say in 1 minute or 1 hour).