Question

A does $\frac{4}{5}$ of a work in $20$ days. He then calls in $B$ and they together finish the remaining work in $3$ days. How long $B$ alone would take to do the whole work?

• A. $23$ days
• B. $37$ days
• C. $37\frac{1}{2}$ days
• D. $40$ days

Answer 1

The correct option is C $37\frac{1}{2}$ days

$A$ does $\frac{4}{5}$ work in $20$ day $\Rightarrow$ In $1$ day $A$ does $\frac{1}{25}$ units of work

$A$ and $B$ do $\frac{1}{5}$ work in $3$ days $\Rightarrow$ In $1$ day $A$ and $B$ do $\frac{1}{15}$ units of work

Say $B$ does $\frac{1}{x}$ units of work in $1$ day.

$\Rightarrow \frac{1}{25}+\frac{1}{x}=\frac{1}{15}$

$\Rightarrow \frac{1}{x}=\frac{1}{15}-\frac{1}{25}=\frac{10}{15\times 25}$

$\therefore$ $x=\frac{15\times 25}{10}=37.5$

$\therefore$ $B$ does the complete work in $x$ days $=37.5$ days

Answer : Option D.