A and B can do a piece of work in $12$ days and $15$ days respectively. They start together, but A leaves after $4$ days. B alone will finish the remaining work in:

Question

A and B can do a piece of work in $12$ days and $15$ days respectively. They start together, but A leaves after $4$ days. B alone will finish the remaining work in:

Option A

5 days

Option B — Correct answer

6 days

Correct choice.

Option C

$\frac{20}{3}$ days

Option D

$\frac{25}{3}$ days

Explanation

In 4 days, both complete $4\left(\frac1{12}+\frac1{15}\right)=4\times\frac{9}{60}=\frac35$ of the work. Remaining work $=\frac25$. B alone takes $\frac{2}{5}\div\frac1{15}=6$ days.

Chapter Mock 7: Time and Work, Pipe and Cistern