To solve the problem, we need to determine how many days C alone will take to finish the job based on the information given about A, B, and C.
### Step-by-Step Solution:
1. **Determine the work done by A and B together in one day**:
- A and B can finish the job in 24 days. Therefore, the work done by A and B in one day is:
\[
\text{Work of A and B in one day} = \frac{1}{24}
\]
2. **Determine the work done by A, B, and C together in one day**:
- A, B, and C can finish the job in 8 days. Therefore, the work done by A, B, and C in one day is:
\[
\text{Work of A, B, and C in one day} = \frac{1}{8}
\]
3. **Calculate the work done by C alone in one day**:
- To find the work done by C alone, we can subtract the work done by A and B from the work done by A, B, and C:
\[
\text{Work of C in one day} = \text{Work of A, B, and C in one day} - \text{Work of A and B in one day}
\]
\[
\text{Work of C in one day} = \frac{1}{8} - \frac{1}{24}
\]
4. **Finding a common denominator**:
- The least common multiple (LCM) of 8 and 24 is 24. We can rewrite the fractions:
\[
\frac{1}{8} = \frac{3}{24}
\]
\[
\frac{1}{24} = \frac{1}{24}
\]
- Now substituting these values:
\[
\text{Work of C in one day} = \frac{3}{24} - \frac{1}{24} = \frac{2}{24} = \frac{1}{12}
\]
5. **Determine how many days C will take to finish the job alone**:
- If C can do \(\frac{1}{12}\) of the work in one day, then the total time taken by C to complete the job alone is the reciprocal of \(\frac{1}{12}\):
\[
\text{Days taken by C} = 12 \text{ days}
\]
### Final Answer:
C alone will finish the job in **12 days**.
