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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?









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Option(B) is correct

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 \(\left(\dfrac{1}{8}\right)^{th}\) of the tank in an hour.

Hence, $n$ fill pipes will fill \(\left(\dfrac{n}{8}\right)^{th}\)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 \(\left(\dfrac{1}{6}\right)^{th}\)

of the tank in an hour.

Therefore, $(8−n)$ waste pipes will drain \(\left(\dfrac{8-n}{6}\right)^{th}\)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,

\(\left(\dfrac{1}{6}\right)^{th}\) 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) 

\(=\left(\dfrac{1}{6}\right)^{th}\)capacity of the tank drained in 1 hour.



$⇒ 14n−64=−8$ 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).

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