Question

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was :

• A. $4$
• B. $8$
• C. $9$
• D. $12$

Answer 1

The correct option is A $4$

$A$ can complete the work in $45$ days

Work done by $A$ in one day is $\frac{1}{45}$

$A$ and $B$ can complete the wrok in $40$ days

Work done by $A$ and $B$ in one day is $\frac{1}{40}$

Let the number of days worked by $A$ be $x$

Total number of days is $23$

From the given conditions

$⟹\frac{x}{45}+\frac{23}{40}=1⟹\frac{x}{45}=\frac{17}{40}⟹x=19\frac{1}{8}$

Number of days after $A$ left the work is $23-19\frac{1}{8}=3\frac{7}{8}$