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?
Answers
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.