Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

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Answer:Pipe A fills the tank normally in 2 hours.

Therefore, it will fill 12 of the tank in an hour.

Let the leak take x hours to empty a full tank when pipe A is shut.

Therefore, the leak will empty 1x of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak =

12 – 1x of the tank. —– (1)

When there is a leak, the problem states that it takes two and a half hours to fill the tank. i.e. 52hours.

Therefore, in an hour, 25th of the tank gets filled. —– (2)

Equating (1) and (2), we get 12 – 1x = 25

=> 1x = 12 – 25 = 110

=> x = 10 hours.

The problem can also be solved without putting pen to paper as follows.

Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.

When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e 52hours to fill the tank or 25th or 40% of the tank gets filled.

On account of the leak, (50 – 40)% = 10% of the water gets wasted every hour.

Therefore, the leak will take 10 hours to drain a full tank.