5 men and 2 women working together can do four times as much work per hour as a man and a woman together. The work done by a man and a woman should be in the ratio :

Options

A. A) `1:2`
B. B) `2:1`
C. C) `1:3`
D. D) `4:1`

Answer

To solve the problem, we need to establish the relationship between the work done by men and women based on the information given. Let's break it down step by step.

### Step 1: Understand the Given Information
We know that:
- 5 men and 2 women working together can do 4 times as much work per hour as a man and a woman together.

### Step 2: Define Variables
Let:
- The work done by one man in one hour = \( m \)
- The work done by one woman in one hour = \( w \)

### Step 3: Set Up the Equation
From the problem:
- Work done by 5 men and 2 women in one hour = \( 5m + 2w \)
- Work done by 1 man and 1 woman in one hour = \( m + w \)

According to the problem, we have:
\[ 5m + 2w = 4(m + w) \]

### Step 4: Expand and Rearrange the Equation
Expanding the right side:
\[ 5m + 2w = 4m + 4w \]

Now, rearranging the equation:
\[ 5m + 2w - 4m - 4w = 0 \]
\[ m - 2w = 0 \]

### Step 5: Solve for the Ratio
From the equation \( m - 2w = 0 \), we can express \( m \) in terms of \( w \):
\[ m = 2w \]

### Step 6: Establish the Ratio
Now, we can find the ratio of the work done by a man to the work done by a woman:
\[ \frac{m}{w} = \frac{2w}{w} = 2:1 \]

### Conclusion
The ratio of the work done by a man to the work done by a woman is \( 2:1 \).