Question

Two pipes can fill a cistern in 30 and 15 h respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom 5 h extra are taken for cistern to be filled up. If the cistern in full in what time would the leak empty it ?

• A. 10 hours
• B. 20 hours
• C. 30 hours
• D. 40 hours

Answer 1

The correct option is C 30 hours

Part of the istern filled when the two pipes are opened simultaneously $=\frac{1}{30}+\frac{1}{15}=\frac{1+2}{30}=\frac{3}{10}=\frac{1}{10},$

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