Question

Two pipes $A$ and $B$ can separately fill a cistern in $60minutes$ and $75minutes$ respectively. There is a third pipe at the bottom of the cistern to empty it , If all the three pipes are simultancously opened, then the cistern is full in $50minutes$, In how much time, the third pipe alone can empty the cistern ?

• A. $110minutes$
• B. $100minutes$
• C. $120minutes$
• D. $90minutes$

Answer 1

The correct option is B $100minutes$

Let the third pipe empty the whole cistern in x minutes.
$\therefore \frac{1}{60}+\frac{1}{75}-\frac{1}{x}=\frac{1}{50}$
$\Rightarrow \frac{1}{x}=\frac{1}{60}+\frac{1}{75}-\frac{1}{50}=\frac{5+4-6}{300}=\frac{3}{300}=\frac{1}{100}$
The third pipe can empty the cistern in 100 minute