Question

$A$ does $80$% 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. $37\frac{1}{2}$
• D. $40$ days

Answer 1

Answer: (C)

$37\frac{1}{2}$

Whole work is done by $A$ in $(20\times \frac{5}{4})=25$ days.
Now, $(1-\frac{4}{15})$ i.e., $\frac{1}{5}$ work is done by $A$ and $B$ in $3$ days.
Whole work will be done by $A$ and $B$ in $(3\times 5)$ $=15$ days.
$A$'s $1$ day's work $=\frac{1}{25}$, $(A+B)$'s $1$ day's work $=\frac{1}{15}$.
$\therefore$ $B$'s $1$ day's work $=(\frac{1}{15}-\frac{3}{25})=\frac{4}{150}=\frac{2}{75}$
So, $B$ alone would do the work in $\frac{75}{2}=37\frac{1}{2}$ days.