Question

$A$ and $B$ together can complete a work in $3$ days. They start together but after $2$ days, $B$ left the work. If the work is completed after two more days, then $B$ alone could do the whole work in

• A. $8$ days
• B. $3$ days
• C. $2$ days
• D. $6$ days

Answer 1

The correct option is D $6$ days

Let $A$ and $B$ alone complete the whole work in $x$ and $y$ days respectively.
Then, one day work of $A=\frac{1}{x}$
and one day work of $B=\frac{1}{y}$
According to question,
$\frac{3}{x}+\frac{3}{y}=1$
and $\frac{4}{x}+\frac{2}{y}=1$
Solving the above two equations, we get
$x=6$ and $y=6$
So, $B$ alone can complete the whole work in $6$ days.