Question

Two pipes can fill a cistern in $12$ and $20$ hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, $30$ minutes extra are taken for the cistern to be filled up. If the cistern is full, what time would the leak take to empty it?

• A. $120$ hours
• B. $100$ hours
• C. $110$ hours
• D. $115$ hours

Answer 1

The correct option is A $120$ hours

Cistern filled by both pipes in one hour $=\frac{1}{12}+\frac{1}{20}=\frac{2}{15}$
Therefore both pipes filled the cistern in $\frac{15}{2}$ hrs.
Now, due to leakage, both pipes filled the cistern in $\frac{15}{2}+\frac{30}{60}=8$ hrs.
Therefore due to leakage, part filled in one hour $=\frac{1}{8}$
Therefore part of cistern emptied, due to leakage in one hour $=\frac{2}{15}-\frac{1}{8}=\frac{1}{120}$
Hence, in $120$ hours, the leak would empty the cistern.