Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened the cistern is full in 50 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 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern?

Solution:
Let the third pipe can empty the cistern in x min

According to the question,
⇒ (1/60) + (1/75) - (1/x) = 1/50
⇒ (1/60) + (1/75) - (1/50) = 1/x
⇒ (5 + 4 - 6)/300 = 1/x
⇒ 3/300 = 1/x
∴ x = 100

So, the third pipe will empty the full cistern in 100 min.