A water tank has two inlet taps which fill it in 20 minutes and 30 minutes, respectively and there is an outlet tap. When all the three taps are opened together, it takes 60 minutes to fill an empty cistern. How long will the outlet tap take to empty it?

The inlet taps fill at rates of 1/20 and 1/30 of the tank per minute. Combined, they fill at (1/20 + 1/30) = 5/60 = 1/12 per minute. With the outlet tap open, the net fill rate becomes 1/60 per minute (given). If the outlet empties in x minutes, then 1/12 - 1/x = 1/60. Solving: 1/x = 1/12 - 1/60 = 4/60 = 1/15, so x = 15 minutes.