Question

A and B can do a piece of work in 45 and 40 days, respectively. They began the work together, but A leaves after some days and B finished the remaining work in 23 days. After how many days, did A leaves?

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

Answer 1

The correct option is C 9 days

B's 23 days' work
$=\frac{23}{40}$

$Reaminingwork=1-\frac{23}{40}=\frac{17}{40}$

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

$\frac{17}{360}\text{work is done by A and B in 1 day}$

$\therefore$ $\frac{17}{40}\text{work is done by A and B in}$

$\frac{360\times 17}{17\times 40}=9days.$

So, A left after 9 days.