A can do a piece of work in 3 days while B can do the same work in 4 days. If they work together for a total wages of Rs. 2800, how much does A get?

Options

A. X 1200
B. X 1900
C. X 1300
D. X 1600

Answer

To solve the problem step by step, we will first determine the work efficiency of A and B, then calculate their respective shares of the total wages based on their efficiencies.

### Step-by-Step Solution:

1. **Determine the work done by A and B:**
- A can complete the work in 3 days. Therefore, A's work rate (efficiency) is:
\[ \text{Efficiency of A} = \frac{1 \text{ work}}{3 \text{ days}} = \frac{1}{3} \text{ work per day} \]
- B can complete the work in 4 days. Therefore, B's work rate (efficiency) is:
\[ \text{Efficiency of B} = \frac{1 \text{ work}}{4 \text{ days}} = \frac{1}{4} \text{ work per day} \]

2. **Find the combined efficiency of A and B:**
- To find the total efficiency when A and B work together, we add their efficiencies:
\[ \text{Combined Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} = \frac{1}{3} + \frac{1}{4} \]
- To add these fractions, we need a common denominator. The LCM of 3 and 4 is 12:
\[ \frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12} \]
- Therefore,
\[ \text{Combined Efficiency} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \text{ work per day} \]

3. **Calculate the total work done in terms of efficiency:**
- Since A's efficiency is 4 and B's efficiency is 3 (from the LCM calculation), the ratio of their efficiencies is:
\[ \text{Ratio of A's efficiency to total efficiency} = \frac{4}{7} \]
\[ \text{Ratio of B's efficiency to total efficiency} = \frac{3}{7} \]

4. **Calculate A's share of the total wages:**
- The total wages for the work done is Rs. 2800. A's share of the wages can be calculated as follows:
\[ \text{A's share} = \text{Total Wages} \times \text{Ratio of A's efficiency} = 2800 \times \frac{4}{7} \]
- Now, calculating A's share:
\[ \text{A's share} = 2800 \times \frac{4}{7} = 2800 \times 0.5714 = 1600 \]

5. **Final Answer:**
- Therefore, A gets Rs. 1600.

### Summary:
A's share of the total wages is Rs. 1600.