Question

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They begin together but $A$ leaves after some days and $B$ completes the rest in $23$ days. For how many days did $A$ work ?

• A. $6$ days
• B. $9$ days
• C. $8$ days
• D. $12$ days

Answer 1

Answer: (B)

$9$ days

A's one day's work $=\frac{1}{45}$

B's one day's work $=\frac{1}{40}$

$\therefore (A+B)$'s 1 day's work $=\frac{1}{45}+\frac{1}{40}=\frac{8+9}{360}=\frac{17}{360}$

Work done by B in 23 days $=\frac{1}{40}\times 23=\frac{23}{30}$
Remaining work $=1-\frac{23}{40}=\frac{40-23}{40}=\frac{17}{40}$
$(A+B)$'s 1 day work $=\frac{17}{360}$
$\frac{17}{40}$ work done by $(A+B)$ in $1\times \frac{360}{17}\times \frac{17}{40}=9Days$