2 men and 1 woman together can complete a piece of work in 14 days, while 4 women and 2 men together can do it in 8 days. If a man gets ₹ 600 per day. how much should a woman get per day?

Options

A. ₹ 400
B. ₹ 450
C. ₹ 480
D. ₹ 360

Answer

To solve the problem step by step, we will first establish the work done by men and women based on the information provided.

### Step 1: Determine the work done by men and women
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:
- 2 men and 1 woman can complete the work in 14 days.
- Therefore, the total work can be expressed as:
\[ \text{Total Work} = (2M + W) \times 14 \]

- 4 women and 2 men can complete the work in 8 days.
- Therefore, the total work can also be expressed as:
\[ \text{Total Work} = (4W + 2M) \times 8 \]

### Step 2: Set the equations equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ (2M + W) \times 14 = (4W + 2M) \times 8 \]

### Step 3: Simplify the equation
Expanding both sides gives:
\[ 28M + 14W = 32W + 16M \]

Now, rearranging the equation to group like terms:
\[ 28M - 16M = 32W - 14W \]
\[ 12M = 18W \]

### Step 4: Find the ratio of M to W
Dividing both sides by 6 gives:
\[ 2M = 3W \]
Thus, we can express \( M \) in terms of \( W \):
\[ M = \frac{3}{2}W \]

### Step 5: Determine the daily wage of a woman
Given that a man earns ₹600 per day, we can substitute \( M \) into the equation:
\[ \frac{3}{2}W = 600 \]

### Step 6: Solve for W
To find \( W \):
\[ W = 600 \times \frac{2}{3} = 400 \]

### Conclusion
Thus, the daily wage of a woman should be ₹400.