Two pipes can fill a tank in 12 hours and 24 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the tank, it took 2 hours more to fill the tank. When the tank is completely full, in what time will the leak empty it?
1). 34 hours
2). 36 hours
3). 38 hours
4). 40 hours
Let the leak empty the tank in h hours.
∴ In 1 hr, it empties 1/h part.
Given, two pipes can fill a tank in 12 hours and 24 hours respectively
1 hr, they can fill 1/12 and 1/24 part respectively.
Thus, working together, in 1 hr part of tank they can fill = 1/12 + 1/24 = 1/8
∴ They can fill the tank in 8 hours.
Now due to the leak it took 2 hours more.
Thus, the tank was filled in 10 hours.
In 1hr, part of tank filled = 1/10
⇒ 1/8 – 1/h = 1/10
⇒ 1/8 – 1/10 = 1/h
⇒ h = 40 hours