Two pipes A and B can separately fill a cistern in 40 minutes and 30 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 20 minutes. In how much time, the third pipe alone can empty the cistern?

120 min

100 min

140 min

80 min

Explanation:

Part filled by pipe A in 1 minute =$\dfrac{1}{40}$

Part filled by pipe B in 1 minute $=\dfrac{1}{30}$

Net part filled by pipe A, pipe B and the third pipe together in 1 minute =$\dfrac{1}{20}$

Therefore, part emptied by the third pipe in 1 minute =$\dfrac{1}{40}+\dfrac{1}{30}-\dfrac{1}{20}=\dfrac{3+4-6}{120}=\dfrac{1}{120}$

i.e., third pipe alone can empty the cistern in 120 minutes.