- 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?
(1) 2 hours 30 minutes (2) 5 hours (3) 4 hours (4) 10 hours
Solution:
Pipe A fills the tank normally in 2 hours. Therefore, it will fill
� 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
1/4
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 =
1/2 -1/x
of the tank. � (1)
When there is a leak, the problem states that Pipe A takes two and a half hours
to fill the tank. i.e.
5/2
hours. Therefore, in an hour,
5/2 th
of the tank gets filled. � (2)
Equating (1) and (2), we get 1/2 - 1/x =2/5=>
1/x = 1/2 - 2/5 = 1/10
=> x = 10 hours.
The problem can also be mentally done 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 5/2
hours to fill the tank or
2/5 th
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.
