Part of the cistern filled when the two pipes are opened simultaneously = \(\frac{1}{30}\)+ \(\frac{1}{15}\) = \(\frac{1+2}{30}\) = \(\frac{3}{30}\) = \(\frac{1}{10}\) i.e, The two pipes can fill the cistern together in 10 hours
Together with the leak, the cistern can be filled in (10 + 5) hours = 15 hours
Let the leak take x hours to empty the cistern. Then,
\(\frac{1}{10}\) - \(\frac{1}{X}\) = \(\frac{1}{15}\) \(\Rightarrow\) \(\frac{1}{X}\) = \(\frac{1}{10}\) - \(\frac{1}{15}\) = \(\frac{1}{30}\)
\(\therefore\) The leak takes 30 hours to empty the cistern