Question

Pipes $A$ and $B$ can fill a tank in $5$ and $6$ hours respectively. Pipe $C$ can empty it in $12$ hours. If all the three pipes are opened together, then the tank will be filled in

• A. $3\frac{9}{17}$ hours
• B. $2\frac{8}{17}$ hours
• C. $1\frac{13}{17}$ hours
• D. $4\frac{1}{2}$ hours

Answer 1

The correct option is A $3\frac{9}{17}$ hours

Part filled by $A$ in $1$ hour $=\frac{1}{5}$
Part filled by $B$ in $1$ hour $=\frac{1}{6}$
Part emptied by $C$ in $1$ hour $=\frac{1}{12}$
Net part filled in $1$ hour $=\frac{1}{5}+\frac{1}{6}-\frac{1}{12}=\frac{17}{60}$
$\therefore$ The tank will be full in $\frac{60}{17}$ hours
i.e., $3\frac{9}{17}$ hours.