A,B and C can do a piece of work in 12,18 and 9 days respectively. A started the work and worked for 4 days. Then B alone worked for 2 days. How many days would C alone take to complete the remaining work?

Options

A. 5
B. 4
C. 3
D. 6

Explanation

To solve the problem step by step, we will first determine the work done by A, B, and C in one day, then calculate the total work done by A and B, and finally find out how many days C will take to complete the remaining work.

### Step-by-Step Solution:

1. **Determine the Work Rates**:
- A can complete the work in 12 days, so A's one day work = \( \frac{1}{12} \).
- B can complete the work in 18 days, so B's one day work = \( \frac{1}{18} \).
- C can complete the work in 9 days, so C's one day work = \( \frac{1}{9} \).

2. **Calculate Work Done by A in 4 Days**:
- Work done by A in 4 days = \( 4 \times \frac{1}{12} = \frac{4}{12} = \frac{1}{3} \).

3. **Calculate Work Done by B in 2 Days**:
- Work done by B in 2 days = \( 2 \times \frac{1}{18} = \frac{2}{18} = \frac{1}{9} \).

4. **Calculate Total Work Done by A and B**:
- Total work done by A and B = Work done by A + Work done by B
- Total work = \( \frac{1}{3} + \frac{1}{9} \).
- To add these fractions, find a common denominator (which is 9):
- \( \frac{1}{3} = \frac{3}{9} \)
- So, \( \frac{1}{3} + \frac{1}{9} = \frac{3}{9} + \frac{1}{9} = \frac{4}{9} \).

5. **Calculate Remaining Work**:
- Total work = 1 (the whole work).
- Remaining work = Total work - Work done by A and B
- Remaining work = \( 1 - \frac{4}{9} = \frac{5}{9} \).

6. **Calculate Days Required by C to Complete Remaining Work**:
- C's one day work = \( \frac{1}{9} \).
- Let \( x \) be the number of days C will take to complete the remaining work.
- Work done by C in \( x \) days = \( x \times \frac{1}{9} \).
- Set this equal to the remaining work:
- \( x \times \frac{1}{9} = \frac{5}{9} \).
- Multiply both sides by 9:
- \( x = 5 \).

### Final Answer:
C will take **5 days** to complete the remaining work.