Question

$A$ and $B$ can do a piece of work in $15$ days; $B$ and $C$ in $12$ days; $C$ and $A$ in $20$ days. How many days will be taken by $A,B$ and $C$ working together to finish the work?

Answer 1

Given:

$A$ and $B$ can do a work in $15$ days.

$\Rightarrow$ $(A+B)$'s $1$ day work $=\frac{1}{15}$

$B$ and $C$ can do a work in $12$ days.

$\Rightarrow$ $(B+C)$'s $1$ day work $=\frac{1}{12}$

$C$ and $A$ can do a work in $20$ days.

$\Rightarrow$ $(C+A)$ 's 1 day work $=\frac{1}{20}$

$(A+B+C)$'s $1$ day work $=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}$

$=\frac{4+5+3}{60}$

$=\frac{12}{60}$

$=\frac{1}{5}$

Therefore, $A,B$ and $C$ can finish the work together in $5$ days.