Question

$A$ and $B$ can do a work in 45 days and 40 days respectively. They began the work together but $A$ left after sometime and $B$ completed the remaining work in 23 days. After how many days of start of the work did $A$ leave?

Answer 1

$A$'s 1 days' work $=\frac{1}{45},B$'s 1 days' work $=\frac{1}{40}$
Suppose $A$ left the work after $x$ days of the start of the work. Then,
Work done by $A$ in $x$ days $=\frac{x}{45}$
Work done by $B$ in $(x+23)$ days $=\frac{(x+23)}{40}$
Given, $\frac{x}{45}+\frac{(x+23)}{40}=1\Rightarrow \frac{(8x+9x+207)}{360}=1$
$\Rightarrow 17x=360-207=153\Rightarrow x=\frac{153}{17}=9$ days
$\therefore A$ left after 9 days of start of work.