Question

A tank can be filled by pipe A in $5$ hours and by pipe B in $8$ hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in $20$ hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?

Answer 1

Let Volume of Tank be $V$

pipe $A$ can fill the tank $\frac{V}{5}$ in 1 Hour

pipe $B$ can fill the tank $\frac{V}{8}$ in 1 Hour

$Drainage$ $Hole$ can empty the tank $\frac{V}{20}$ in 1 Hour

$\Rightarrow \frac{V}{5}+\frac{V}{8}-\frac{V}{20}=\frac{V}{T}$

where $\frac{V}{T}$ is the Volume filled when $2$ pipes and $1$ hole is opened, in 1 Hour

$\Rightarrow \frac{1}{5}+\frac{1}{8}-\frac{1}{20}=\frac{1}{T}$

solving we get $T=\frac{40}{11}hrs$