Question

$A$ can do a piece of work in $12$ days while $B$ can do it in $8$ days. With the help of $C,$ they finish the work in $4$ days. Then, $C$ alone can do the work in

Answer 1

$A$ can do the work in $12$ days.

$B$ can do it in $8$ days.

Let $C$ can do the work in $x$ days.

Then,

$\frac{1}{12}+\frac{1}{8}+\frac{1}{x}=\frac{1}{4}$

$\frac{1}{x}=\frac{1}{4}-\frac{1}{12}-\frac{1}{8}$

$\frac{1}{x}=\frac{6-2-3}{24}$

$\frac{1}{x}=\frac{1}{24}$

$x=24$

Hence, $C$ alone can do the work in $24$ days.