A can do 40% of a work in 12 days, whereas B can do 60% of the same work in 15 days. Both work together for 10 days. C completes the remaining work alone in 4 days. A, B and C together will complete 28% of the same work in :

Options

A. `2 1/2` days
B. 3 days
C. `1 1/2` days
D. 2 days

Answer

To solve the problem step by step, we will calculate the efficiencies of A, B, and C, the total work done, and then determine how long A, B, and C together will take to complete 28% of the work.

### Step 1: Calculate the efficiencies of A and B

1. **A's Efficiency**:
- A can do 40% of the work in 12 days.
- Therefore, A can do 100% of the work in \( \frac{12 \text{ days}}{0.4} = 30 \text{ days} \).
- A's efficiency = \( \frac{100}{30} = \frac{10}{3} \) % of work per day.

2. **B's Efficiency**:
- B can do 60% of the work in 15 days.
- Therefore, B can do 100% of the work in \( \frac{15 \text{ days}}{0.6} = 25 \text{ days} \).
- B's efficiency = \( \frac{100}{25} = 4 \) % of work per day.

### Step 2: Calculate the combined efficiency of A and B

- Combined efficiency of A and B = \( \frac{10}{3} + 4 = \frac{10}{3} + \frac{12}{3} = \frac{22}{3} \) % of work per day.

### Step 3: Calculate the total work done by A and B in 10 days

- Work done by A and B in 10 days = \( 10 \times \frac{22}{3} = \frac{220}{3} \) % of work.

### Step 4: Calculate the remaining work

- Total work = 100% (or 150 units).
- Work completed by A and B = \( \frac{220}{3} \) %.
- Remaining work = \( 100 - \frac{220}{3} = \frac{300 - 220}{3} = \frac{80}{3} \) % of work.

### Step 5: Calculate C's efficiency

- C completes the remaining work in 4 days.
- Therefore, C's efficiency = \( \frac{80/3}{4} = \frac{20}{3} \) % of work per day.

### Step 6: Calculate the combined efficiency of A, B, and C

- Combined efficiency of A, B, and C = \( \frac{10}{3} + 4 + \frac{20}{3} = \frac{10 + 12 + 20}{3} = \frac{42}{3} = 14 \) % of work per day.

### Step 7: Calculate the time taken to complete 28% of the work

- Work to be completed = 28% of total work = \( 28 \) %.
- Time taken = \( \frac{28}{14} = 2 \) days.

### Final Answer

A, B, and C together will complete 28% of the work in **2 days**.

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