Question

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

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

Answer 1

The correct option is B $10$ days

Work done by $X$ in $4$ days $=(\frac{1}{20}\times 4)=\frac{1}{5}$
Remaining work $=(1-\frac{1}{5})=\frac{4}{5}$
$(X+Y)$'s $1$ day's work $=(\frac{1}{20}+\frac{1}{12})=\frac{8}{60}=\frac{2}{15}$
Now, $\frac{2}{15}$ is work done by $X$ and $Y$ in $1$ day.
So, $\frac{4}{5}$ work will be done by $X$ and $Y$ in $(\frac{15}{2}\times \frac{4}{5})=6$ days.
Hence, total time taken $=(6+4)$ days $=10$ days.