Question

Tap $A$ can fill a cistern in $8$ hours and tap $B$ can empty it in $12$ hours. How long will it take to fill cistern if both of them are opened together?

Answer 1

Tap $A$ can fill the cistern in $8$ hrs.

Therefore Tap $A$ can do $\frac{1}{8}$ work in $1$ hr.

Tap $B$ can empty the cistern in $12$ hrs.

Therefore Tap $B$ can do $\frac{1}{12}$ work in $1$ hr.

Since $B$ is doing the work of emptying it will be $-\frac{1}{12}$

$\therefore$ total work done when both the cistern are open is $\frac{1}{8}+(-\frac{1}{12})$

$=\frac{1}{8}-\frac{1}{12}$

$=\frac{3-2}{24}$ (Taking LCM)

$=\frac{1}{24}$

Therefore it will take $24$ hrs to fill the cistern if both are opened.