A, B and C can complete the work in 4, 5 and 6 hours respectively. If they all work together and receive Rs. 777 as wages, then find the share of A
A. Rs. 300
B. Rs. 315
C. Rs. 326
D. Rs. 175

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem, we need to determine the share of A when A, B, and C work together and receive a total of Rs. 777 as wages.

### Step-by-Step Solution:

1. **Determine the Work Rates of A, B, and C:**
- A can complete the work in 4 hours, so A's work rate is \( \frac{1}{4} \) of the work per hour.
- B can complete the work in 5 hours, so B's work rate is \( \frac{1}{5} \) of the work per hour.
- C can complete the work in 6 hours, so C's work rate is \( \frac{1}{6} \) of the work per hour.

2. **Calculate the Combined Work Rate:**
- The combined work rate of A, B, and C when working together is:
\[ \text{Combined Work Rate} = \frac{1}{4} + \frac{1}{5} + \frac{1}{6} \]
- To add these fractions, find a common denominator. The least common multiple of 4, 5, and 6 is 60.
- Convert each fraction:
\[ \frac{1}{4} = \frac{15}{60}, \quad \frac{1}{5} = \frac{12}{60}, \quad \frac{1}{6} = \frac{10}{60} \]
- Now add them:
\[ \text{Combined Work Rate} = \frac{15 + 12 + 10}{60} = \frac{37}{60} \]

3. **Determine the Efficiency Ratio:**
- The efficiency ratio of A, B, and C is proportional to their work rates:
- A's efficiency = 15
- B's efficiency = 12
- C's efficiency = 10
- Therefore, the efficiency ratio is 15:12:10.

4. **Calculate Total Parts of the Ratio:**
- Total parts = 15 + 12 + 10 = 37 parts.

5. **Calculate the Share of A:**
- Since the total wages are Rs. 777, we can find the value of one part:
\[ \text{Value of one part} = \frac{777}{37} = 21 \]
- Now, calculate A's share:
\[ \text{A's Share} = 15 \times 21 = 315 \]

### Final Answer:
A's share of the wages is Rs. 315.