Two pipes P and Q can separately fill a cistern in 20 and 30 minutes respectively. There is another exhaust pipe R at the bottom of the cistern. If all the three pipes are opened at the same time, the cistern will be full in 24 minutes. The time (in minutes) for the pipe R to
empty the full cistern is

Let the capacity of the cistern be 600 liters
Hence, capacity of pipe P = 30 liters/min and capacity of Q = 20 liters/min 
Let the draining capacity of R be -r liters per minute. 

Now, when all three are opened together, the cistern gets filled in 24 minutes.
Effective capacity of all three together = 600/24 = 25 liters/min

Hence, 30+20-r = 25 ===> r = 25 liters/min
Hence, time required by R to empty complete cistern =  600/25 = 24 minutes