A tank is fitted with 8 pipes some of which that fill the tank and others that empty the tank Each o...........

Quantitative Aptitude ( CCS) Pipes&cistern

A tank is fitted with 8 pipes, some of which that fill the tank and others that empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of those that empty the tank empties it in 6 hours. If all the pipes are kept open when the tank is full, it will take 6 hours to drain the tank. How many of these are fill pipes?

2 fill pipes

4 fill pipes

6 fill pipes

8 fill pipes

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Explanation:

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 1/8th of the tank in an hour.

n fill pipes will fill n/8th of the tank in an hour.

Similarly, each of the waste pipes will drain the full tank in 6 hours.
∴ each of the waste pipes will drain 1/6th of the tank in an hour.

(8 - n) waste pipes will drain (8−n)/6th 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, 1/6th 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) = 1/6th of the tank

n/8 - (8−n)/6 = −1/6
Note: The right hand side has a negative sign because the tank gets drained.

Cross multiplying and solving the equations, 14n - 64 = -8
Or 14n = 56 or n = 4

Hence, option 2 is the correct answer.