Three men and two women can do a piece of work in 4 days, while two men and three women can, do the same work in 5 days. ₹ 44 is given to a woman for her contribution towards work, per day. What, is the amount received by a man per day?

Options

A. ₹ 88
B. ₹ 144
C. ₹ 154
D. can’t be determined

Answer

To solve the problem, we need to determine the amount received by a man per day based on the information provided about the work done by men and women.

### Step-by-Step Solution:

1. **Understanding the Work Done**:
- Let the work done by one man in one day be \( M \) and the work done by one woman in one day be \( W \).
- According to the problem, 3 men and 2 women can complete the work in 4 days. Therefore, the total work can be expressed as:
\[ \text{Total Work} = (3M + 2W) \times 4 \]
- Similarly, 2 men and 3 women can complete the same work in 5 days:
\[ \text{Total Work} = (2M + 3W) \times 5 \]

2. **Setting Up the Equations**:
- From the first scenario:
\[ 12M + 8W = \text{Total Work} \quad (1) \]
- From the second scenario:
\[ 10M + 15W = \text{Total Work} \quad (2) \]

3. **Equating the Total Work**:
- Since both expressions represent the same total work, we can set them equal to each other:
\[ 12M + 8W = 10M + 15W \]

4. **Simplifying the Equation**:
- Rearranging gives:
\[ 12M - 10M = 15W - 8W \]
\[ 2M = 7W \]
- This implies:
\[ M = \frac{7}{2}W \quad (3) \]

5. **Finding the Daily Wage of Men**:
- We know that a woman earns ₹ 44 per day. Therefore:
\[ W = 44 \]
- Substituting \( W \) into equation (3):
\[ M = \frac{7}{2} \times 44 = \frac{308}{2} = 154 \]

6. **Conclusion**:
- The amount received by a man per day is ₹ 154.

### Final Answer:
The amount received by a man per day is ₹ 154.