Question

Two pipes $A$ and $B$ can fill a cistern in 20 minutes and 25 minutes respectively. Both are opened together but at the end of 5 minutes $B$ is turned off. What is the total time taken to fill the cistern?

Answer 1

Part of the cistern filled by $(A+B)$ in one minute $=\left(\frac{1}{20}+\frac{1}{25}\right)=\frac{5+4}{100}=\frac{9}{100}$

$\therefore$ Part of the cistern filled by $(A+B)$ in 5 minutes $=5\times \frac{9}{100}=\frac{9}{20}$

Remaining part $=1-\frac{9}{20}=\frac{11}{20}$

$\frac{1}{20}$ part of the cistern is filled by $A$ in a minute

$\therefore \frac{11}{20}$ part of the cistern is filled by $A$ in $20\times \frac{11}{20}$ minutes $=11$ minutes

$\therefore$ Total time taken to fill the cistern $=(11+5)=16$ min