(c) 8640 litres
Suppose the cistern holds x litres of water. The tap admits 6 litres of water in 1 minute, i.e., it admits 360 litres of water in 1hour.
\(\therefore\) x litres of water can be filled in \(\frac{X}{360}\) hours.
The leak would empty the tank in 8 hours.
\(\therefore\) In one hour, \(\frac{1}{8}\) of the tank becomes empty.
If the tap and the leak both are allowed simultaneously, then the tank becomes empty in 12 hours, i.e.,
\(\frac{1}{8}-\frac{360}{X}\) = \(\frac{1}{12}\) \(\Rightarrow\) \(\frac{360}{X}\) = \(\frac{1}{8}\) - \(\frac{1}{12}\) = \(\frac{3-2}{24}\) = \(\frac{1}{24}\)
\(\Rightarrow\) x = (360 × 24) litres = 8640 litres.
