Question

$A$ and $B$ can complete a task in $12$ days. However, $A$ had to leave a few days before the task was complete and hence it took $16$ days in all to complete task. If $A$ alone could complete the work in $21$ days, how many days before the work getting over did $A$ leave?

• A. $7$
• B. $9$
• C. $5$
• D. $0$

Answer 1

The correct option is A $7$

B can alone do the work

$=\frac{1}{\frac{1}{12}-\frac{1}{21}}$ days

$⟹\frac{1}{B}=\frac{7-4}{84}=\frac{3}{84}=\frac{1}{28}$

$=28$ Days

Let $A$ worked $X$ days, So

Work done by $A+$ Work done by $B=1$

$\frac{X}{21}+\frac{16}{28}=1$

$⟹\frac{X}{21}=\frac{12}{28}$

$⟹X=9$

Hence, $A$ worked for $9$ days means $A$ left work before $(16-9)=7$ days of completion.