A and B can complete a piece of work in 12 days and 18 days respectively. They start working together, but after 4 days, A leaves the work. In how many days will B alone complete the remaining work?

The correct answer is 8.

Step 1: Determine the daily work rate of A and B.
Let the total work be represented as 1 unit.
A can complete the work in 12 days, so A's work rate per day is:

$\frac{1}{12}$

B can complete the work in 18 days, so B's work rate per day is:

$\frac{1}{18}$

Step 2: Calculate the combined work done in the first 4 days.
Working together, the combined work done by A and B in 1 day is:

$\frac{1}{12}+\frac{1}{18}=\frac{3+2}{36}=\frac{5}{36}$

In 4 days, the amount of work completed by A and B together is:

$4\times \frac{5}{36}=\frac{20}{36}=\frac{5}{9}$

Step 3: Find the remaining work.
The remaining work after A leaves is:

$1-\frac{5}{9}=\frac{4}{9}$

Step 4: Calculate the time taken by B to finish the remaining work.
Since B completes $\frac{1}{18}$ of the work in 1 day, the time taken by B alone to complete the remaining $\frac{4}{9}$ of the work is:

$\text{Days required}=\frac{\frac{4}{9}}{\frac{1}{18}}=\frac{4}{9}\times 18=8\text{days}$

Thus, B alone will complete the remaining work in 8 days.