2 men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 90 per day, what should be the wages per day of a women?

Options

A. `Rs.48`
B. `Rs.60`
C. `Rs.72`
D. `Rs.135`

Answer

To solve the problem step by step, we will denote the work done by a man in one day as \( m \) and the work done by a woman in one day as \( w \).

### Step 1: Set up the equations based on the information given.

From the first part of the question, we know that:
- 2 men and 1 woman can complete the work in 14 days.

This means the total work can be expressed as:
\[ \text{Total Work} = (2m + 1w) \times 14 \]
Let’s denote the total work as \( W \):
\[ W = 14(2m + w) \quad \text{(Equation 1)} \]

From the second part of the question, we know that:
- 4 women and 2 men can complete the work in 8 days.

This means the total work can be expressed as:
\[ W = (4w + 2m) \times 8 \]
So we have:
\[ W = 8(4w + 2m) \quad \text{(Equation 2)} \]

### Step 2: Set the two equations equal to each other.

Since both equations represent the same total work \( W \), we can set them equal to each other:
\[ 14(2m + w) = 8(4w + 2m) \]

### Step 3: Expand both sides of the equation.

Expanding both sides gives:
\[ 28m + 14w = 32w + 16m \]

### Step 4: Rearrange the equation to isolate terms.

Now, we will move all terms involving \( m \) to one side and all terms involving \( w \) to the other side:
\[ 28m - 16m = 32w - 14w \]
This simplifies to:
\[ 12m = 18w \]

### Step 5: Simplify the ratio of men to women.

Dividing both sides by 6 gives us:
\[ 2m = 3w \]
Thus, we can express \( w \) in terms of \( m \):
\[ \frac{w}{m} = \frac{2}{3} \]

### Step 6: Calculate the wages of a woman.

Given that a man earns Rs. 90 per day, we can find the wage of a woman. Let \( x \) be the wage of a woman:
\[ \frac{x}{90} = \frac{2}{3} \]

### Step 7: Cross-multiply to solve for \( x \).

Cross-multiplying gives:
\[ 3x = 2 \times 90 \]
\[ 3x = 180 \]

### Step 8: Solve for \( x \).

Dividing both sides by 3:
\[ x = \frac{180}{3} = 60 \]

### Conclusion:

The wage per day of a woman is Rs. 60.

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