Question

$A$ and $B$ can do a piece of work in $20$ days and $12$ days respectively. $A$ started the work alone and then after $4$ days. $B$ joined him till the completion of the work. How long did the work last.?

• A. $10$ days
• B. $20$ days
• C. $15$ days
• D. $6$ days

Answer 1

Answer: (A)

$10$ days

$A$'s one days' work $=$ $\frac{1}{20}$.

$B$'s one days' work $=$ $\frac{1}{12}$.

Work done by $A$ in $4$ days $=$ $\frac{4}{20}=\frac{1}{5}$.
Remaining work $=$ $1-\frac{1}{5}=\frac{4}{5}$

$(A+B)$'s $1$ days' work $=$ $\frac{1}{20}+\frac{1}{12}=\frac{2}{15}$
$\therefore$ Number of days to do the remaining work $=$ $\frac{4}{5}÷\frac{2}{12}=\frac{4}{5}\times \frac{15}{2}=6$ days
$\therefore$ Total number of days taken in the completion of work $=6+4=10$ days.