The two taps can together fill the cistern in 6 mimutes.
(100/10 + 100/15) * N(minutes) = 100
Solving the equation, N= 6 minutes
In 18 minutes, the two taps can fill the cistern three times. In order to leave it full while the waste pipe is open, it means the full cistern is emptied twice. Therefore the answer is 18/ 2 = 9 minutes