Two pipes A and B can fill a cistern in 15 and 20, respectively. Both the pipes are opened together, but after 2 min, pipe A is turned off. What is the total time required to fill the tank?

Part filled by both in 2 min = 2 x ( 1/15 + 1/20 ) = 2 x ( 4 + 3)/60 = 7/30
Part unfilled = 1 - 7/30 = (30 - 7)/30 = 23/30
Now, B fills 1/20 part in 1 min.
∴ 23/30 part will be filled by B in (20 x 23)/30 min or in 46/3 min.
∴ Required time taken to fill the tank = 2 + 46/3 = 52/3 min.