A,B andC can complete a piece of work in 6,12 and 18 days respectively. A and B started the work and C joined them after one day. B left just 2 days before the completion of the whole work.In how many days was the work completed?

Options

A. 5
B. 4
C. 3
D. 2

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Determine the work done by A, B, and C in one day.
- A can complete the work in 6 days, so A's work per day = Total Work / Days = 36 units / 6 days = 6 units/day.
- B can complete the work in 12 days, so B's work per day = 36 units / 12 days = 3 units/day.
- C can complete the work in 18 days, so C's work per day = 36 units / 18 days = 2 units/day.

### Step 2: Set up the scenario of work done.
- Let \( X \) be the total number of days taken to complete the work.
- A and B work together for the first day.
- C joins A and B after the first day.
- B leaves 2 days before the work is completed.

### Step 3: Calculate the total work done.
- Work done by A and B in the first day = A's work + B's work = 6 units + 3 units = 9 units.
- After the first day, A, B, and C work together for \( X - 2 \) days (since B leaves 2 days before completion).
- Work done by A, B, and C together in one day = A's work + B's work + C's work = 6 units + 3 units + 2 units = 11 units.

### Step 4: Calculate the total work done in terms of \( X \).
- Total work done in \( X - 1 \) days (first day + \( X - 2 \) days) = Work done on first day + Work done in \( X - 2 \) days.
- Total work = 9 units (first day) + 11 units * (X - 2) days = 9 + 11(X - 2).

### Step 5: Set up the equation for total work.
- Total work = 36 units (as assumed).
- Therefore, we can set up the equation:
\[ 9 + 11(X - 2) = 36 \]

### Step 6: Solve for \( X \).
1. Expand the equation:
\[ 9 + 11X - 22 = 36 \]
2. Combine like terms:
\[ 11X - 13 = 36 \]
3. Add 13 to both sides:
\[ 11X = 49 \]
4. Divide by 11:
\[ X = \frac{49}{11} \approx 4.45 \]

Since \( X \) must be a whole number, we round it up to the nearest whole number, which is 5.

### Conclusion:
The work was completed in **5 days**.