Question

If $A$ and $B$ can do a piece of work in $15$ days, $B$ and $C$ can do the same work in $20$ days and $A$ and $C$ can do ti in $30$ days, then $A$ alone can do the work in

• A. $30$ days
• B. $40$ days
• C. $45$ days
• D. $50$ days

Answer 1

The correct option is B $40$ days

$(A+B)$'s work in 1 day$=\frac{1}{15}$; $(B+C)$'s work in 1 day $=\frac{1}{20}$
$(A+C)$'s work in 1 day $=\frac{1}{30}$ $\Rightarrow$ $C$'s work in 1 day $\frac{1}{30}-A$'s work
$\Rightarrow$ $B$'s work in 1 day $\frac{1}{20}-\frac{1}{30}+A$'s work
$\Rightarrow$ $A$'s work $=\frac{1}{15}-\frac{10}{600}-A^{\prime }swork\Rightarrow 2A=\frac{3}{60}\Rightarrow A=\frac{1}{40}$
$\therefore$ He will take $40$ days to complete the work.