A crack at the bottom of a cistern can empty it in 3 hours. A fill tap that fills water at the rate of 10 litres/min is turned on when the cistern is full and now it takes 6 hours for the tank to empty. What is the capacity of the tank?

Correct Answer: 3600 Ltrs.

Let A hours be the time taken by the fill pipe to fill the tank and 8 hours be the time taken for the leak at the bottom of the tank to drain the tank.

Then, 1/A−1/B=−1/6.

We know that 1/B=1/3 (given)

Or 1/A−1/3=−1/6 or 1/A=1/6

Or A = 6 hrs or 360 min.

Capacity of the tank = 10 ltr/min x 360 min = 3600 Itrs.