Question

A, B and C together can do a piece of work in $15$ days, B alone can do it in $30$ days and C alone can do it in $40$ days. In how many days will A alone do the work?

Answer 1

Given,

$(A+B+C)$ can do a piece of work in = $15$ days

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

$B$ alone can do a piece of work in = $30$ days

$B$’s $1$ day work $=\frac{1}{30}$

$C$ alone can do a piece of work in = $40$ days

$C$’s $1$ day work $=\frac{1}{40}$

So,

$A$’s $1$ day work $=\frac{1}{15}-\frac{1}{30}+\frac{1}{40}$

$=\frac{1}{15}-\frac{4+3}{120}=\frac{1}{15}-\frac{7}{120}=\frac{8-7}{120}=\frac{1}{120}$

$\therefore$ $A$ can do a piece of work in $120$ days.