A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Solution:
Clearly, pipe B is faster than pipe A and so,the tank will be emptied.

part to be emptied = 2/5

part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15

1/15 part emptied in 1 minute
∴ Full part emptied in 15 minutes
∴ 2/5 part emptied in (15 × 2)/5 minutes
= 6 minutes

so, the tank will be emptied in 6 min.