Rohit purchased a cistern which had a leakage. The cistern can be filled by two inlet pipes, which can individually fill the cistern in 12 min and 15 min respectively. Despite leakage, the two inlet pipes together can fill the cistern in 20 min. How long will it take to empty the completely full the cistern due to leakage?

Let the capacity of the cistern be LCM of 12 and 15 = 60l

The rate of flow through the inlet pipe 1 = 60/12=5 l/min

The rate of flow through the inlet pipe 2 = 60/15=4 l/min

It is given that despite leakage the two inlet pipes together can fill the cistern in 20 min.

Let the flow through the leakage be x l/min

(5+4-x)20=60

9-x=3

x=6

The leakage will empty the cistern in 60/6=10 min

A is the correct answer.