A and B together can finish a job in 24 days , while A,B and C together can finish can finish the same job in 8 days. C along will finish the job in

Options

A. 12 days
B. 14 days
C. 16 days
D. 24 days

Answer

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**.