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

There are 12 pipes connected to a tank. Some of them are fill pipes and other are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain completely in 6 hours. If all the pipes are kept open, an empty tank get filled in 24 hours. How many of the 12 pipes are filled pipes? Correct Answer 7

Given:

Total number of pipes = 12

Each of the fill pipes can fill the tank = 8 hours

Each drain pipes can drain the tank = 6 hours

Calculations:

Let there be n pipes fill the tank than (12 – n) pipes drain the tank.

In an hour n pipes can fill = n/8

In an hours 12 pipes can drain = (12 – n)/6

⇒ n/8 - (12 – n)/6 = 1/24

⇒ /24 = 1/24

⇒ (3n + 4n – 48)/24 = 1/24

⇒ 7n – 48 = 1

⇒ n = 7

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