A can do a piece of work in 12 days and B in 18 days. They worked together for 4 days, after which A left. In how many more days will B complete the remaining work?

The correct answer is 8.

Step-by-Step Explanation:

1. Determine the work done by A and B per day:
Work done by A in 1 day = $\frac{1}{12}$
Work done by B in 1 day = $\frac{1}{18}$

2. Calculate their combined work per day:
When A and B work together, the portion of work completed in 1 day is:
$\frac{1}{12}+\frac{1}{18}$
Taking the LCM of 12 and 18, which is 36:
$\frac{3+2}{36}=\frac{5}{36}$

3. Calculate the work done in 4 days:
Since they worked together for 4 days:
Work done in 4 days = $4\times \frac{5}{36}=\frac{5}{9}$

4. Find the remaining work:
Total work = 1
Remaining work = $1-\frac{5}{9}=\frac{4}{9}$

5. Calculate the time B takes to finish the remaining work:
B completes 1 unit of work in 18 days.
Time required by B to complete $\frac{4}{9}$ of the work:
$\text{Time}=\frac{4}{9}\times 18=8\text{days}$

Thus, B will take 8 more days to complete the remaining work.