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, we will follow these steps:

### Step 1: Determine the work done by A, B, and C in one day.
- A can complete the work in 12 days, so in one day, A does:
\[ \text{Work done by A in one day} = \frac{1}{12} \text{ of the work} \]

- B can complete the work in 18 days, so in one day, B does:
\[ \text{Work done by B in one day} = \frac{1}{18} \text{ of the work} \]

- C can complete the work in 9 days, so in one day, C does:
\[ \text{Work done by C in one day} = \frac{1}{9} \text{ of the work} \]

### Step 2: Calculate the total work in a common unit.
To make calculations easier, we can assume the total work is 36 units (the least common multiple of 12, 18, and 9).
- Work done by A in one day:
\[ \text{A's work in one day} = \frac{36}{12} = 3 \text{ units} \]

- Work done by B in one day:
\[ \text{B's work in one day} = \frac{36}{18} = 2 \text{ units} \]

- Work done by C in one day:
\[ \text{C's work in one day} = \frac{36}{9} = 4 \text{ units} \]

### Step 3: Calculate the work done by A in 4 days.
- Work done by A in 4 days:
\[ \text{Work done by A} = 4 \times 3 = 12 \text{ units} \]

### Step 4: Calculate the work done by B in 2 days.
- Work done by B in 2 days:
\[ \text{Work done by B} = 2 \times 2 = 4 \text{ units} \]

### Step 5: Calculate the total work done by A and B.
- Total work done by A and B:
\[ \text{Total work done} = 12 + 4 = 16 \text{ units} \]

### Step 6: Calculate the remaining work.
- Remaining work:
\[ \text{Remaining work} = 36 - 16 = 20 \text{ units} \]

### Step 7: Calculate the number of days C will take to complete the remaining work.
- Since C can do 4 units of work in one day, the number of days C will take to complete the remaining work is:
\[ \text{Days taken by C} = \frac{20}{4} = 5 \text{ days} \]

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

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