A and B can complete a work in 40 days, B and C in 60 days and A and C is 48 days. Who is the most efficient worker among A, B and C?

Options

A. A
B. B
C. C
D. Cannot be determined

Answer

To solve the problem, we need to determine the efficiencies of workers A, B, and C based on the information given about how long it takes pairs of them to complete the work together.

### Step-by-Step Solution:

1. **Understand the given information**:
- A and B can complete the work in 40 days.
- B and C can complete the work in 60 days.
- C and A can complete the work in 48 days.

2. **Calculate the work done by pairs**:
- If A and B can complete the work in 40 days, their combined work rate is:
\[ A + B = \frac{1}{40} \text{ (work per day)} \]
- If B and C can complete the work in 60 days, their combined work rate is:
\[ B + C = \frac{1}{60} \text{ (work per day)} \]
- If C and A can complete the work in 48 days, their combined work rate is:
\[ C + A = \frac{1}{48} \text{ (work per day)} \]

3. **Convert these rates to a common denominator**:
- The least common multiple of 40, 60, and 48 is 240.
- Therefore, we can express the work rates as:
- \( A + B = \frac{6}{240} \)
- \( B + C = \frac{4}{240} \)
- \( C + A = \frac{5}{240} \)

4. **Set up equations based on work rates**:
- From the equations:
\[ A + B = 6 \quad (1) \]
\[ B + C = 4 \quad (2) \]
\[ C + A = 5 \quad (3) \]

5. **Add all three equations**:
\[ (A + B) + (B + C) + (C + A) = 6 + 4 + 5 \]
This simplifies to:
\[ 2A + 2B + 2C = 15 \]
Dividing everything by 2 gives:
\[ A + B + C = 7.5 \quad (4) \]

6. **Find individual efficiencies**:
- From equation (1):
\[ A + B = 6 \implies C = 7.5 - 6 = 1.5 \]
- From equation (2):
\[ B + C = 4 \implies A = 7.5 - 4 = 3.5 \]
- From equation (3):
\[ C + A = 5 \implies B = 7.5 - 5 = 2.5 \]

7. **Summarize the efficiencies**:
- A's efficiency = 3.5
- B's efficiency = 2.5
- C's efficiency = 1.5

8. **Determine the most efficient worker**:
- Comparing the efficiencies, A (3.5) is the most efficient worker among A, B, and C.

### Final Answer:
A is the most efficient worker.