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

Let's find the work rates per day for $\text{C}$ and $\text{B}$:
* Work rate of $\text{C}=\frac{1}{18}$ per day
* Work rate of $\text{B}=\frac{1}{24}$ per day

Combined rate when working together:

$$\text{Combined Rate}=\frac{1}{18}+\frac{1}{24}=\frac{4+3}{72}=\frac{7}{72}$$

Work completed by both in $8\text{ days}$:

$$\text{Work Done}=8\times \frac{7}{72}=\frac{7}{9}$$

Calculate the remaining work:

$$\text{Remaining Work}=1-\frac{7}{9}=\frac{2}{9}$$

Time taken by $\text{B}$ alone to complete this remaining work:

$$\text{Time}=\frac{\text{Remaining Work}}{\text{Rate of B}}=\frac{\frac{2}{9}}{\frac{1}{24}}=\frac{2}{9}\times 24=\frac{48}{9}=\frac{16}{3}=5\frac{1}{3}\text{ days}$$