Question

$X$ can do a piece work in $40$ days. He works at it for $8$ days and then $Y$ finished it in $16$ days. How long will they together take to complete the work?

• A. $13\frac{1}{3}$ days
• B. $15$ days
• C. $20$ days
• D. $26$ days

Answer 1

The correct option is A $13\frac{1}{3}$ days

Work done by $X$ in $8$ days $=(\frac{1}{40}\times 8)=\frac{1}{5}$.
Remaining work $=(1-\frac{1}{5})=\frac{4}{5}$.
Now, $\frac{4}{5}$ work done by $Y$ in $16$ days.
Whole work will be done by $Y$ in $(16\times \frac{5}{4})=20$ days.
$\therefore$ $X$'s $1$ day's work $=\frac{1}{40}$,

$Y$'s $1$ day's work $=\frac{1}{20}$.
$(X+Y$)'s $1$ day's work $=(\frac{1}{40}+\frac{1}{20})=\frac{3}{40}$.
Hence $X$ and $Y$ will together complete the work in $\left(\frac{40}{3}\right)=13\frac{1}{13}$ days.