Question

A and B can independently finish a piece fo work in 36 and 45 days respectively. They started working together and after a few days A left. After that B could finish the remaining work in 36 days. After how many days of working together did A leave?

Answer 1

A's one day work $=\frac{1}{36}$
B's one day work $=\frac{1}{45}$
$\therefore$ (A+B)'s one day work $=\frac{1}{36}+\frac{1}{45}=\frac{5+4}{180}=\frac{9}{180}$
Work done by B in $36day=\frac{36}{45}$
$\therefore$ Remaining work $=1-\frac{36}{45}=\frac{9}{45}$
$\therefore$ Number of days A worked $=\frac{9}{45}÷\frac{9}{180}=\frac{9}{45}\times \frac{180}{9}=4$