C and B can do a work in $18$ days and $24$ days respectively. They worked together for $8$ days and then C left. In how many days did B finish the remaining work?

Let's find the total work using the LCM of the days taken by C and B ($18$ and $24$):
$$\text{Total Work}=\text{LCM}(18,24)=72\text{ units}$$

Now, compute the daily work efficiency of C and B:

* Efficiency of C = $\frac{72}{18}=4\text{ units/day}$
* Efficiency of B = $\frac{72}{24}=3\text{ units/day}$

Combined efficiency of C and B working together:

$$\text{Combined Efficiency}=4+3=7\text{ units/day}$$

They worked together for $8$ days, so the work completed in $8$ days is:

$$\text{Work Completed}=7\times 8=56\text{ units}$$

Remaining work after C leaves:

$$\text{Remaining Work}=72-56=16\text{ units}$$

B finishes this remaining work alone. The time taken by B is:

$$\text{Time taken by B}=\frac{\text{Remaining Work}}{\text{Efficiency of B}}=\frac{16}{3}=5\frac{1}{3}\text{ days}$$