Two pipes A and B can separately fill a cistern in 50 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all three pipes are simultaneously opened then the cistern is full in 30 minutes. In how much time the third pipe alone can empty the cistern?

Question: Two pipes A and B can separately fill a cistern in 50 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all three pipes are simultaneously opened then the cistern is full in 30 minutes. In how much time the third pipe alone can empty the cistern?

Solution:
Le the third pipe can empty the cistern in x min.

ATQ,
(1/50) + (1/60) - 1/x = 1/30
⇒ (1/50) + (1/60) - (1/30) = 1/x
⇒ (6 + 5 - 10)/300 = 1/x
⇒ 1/300 = 1/x
∴ x = 300

So, the third pipe will empty the full cistern in 300 min.