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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
5 fill pipes
Answer with explanation
Answer: Option BExplanation
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.
Hence, 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
Therefore,
(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
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