Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is

Options

A. `3y:2x`
B. `2x:3y`
C. `x:y`
D. `2y:3x`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the work done by men and women
We know that:
- Two men can complete a piece of work in \( x \) days.
- \( y \) women can complete the same piece of work in 3 days.

### Step 2: Calculate the total work done
Let's denote the total work as \( W \).

The work done by 2 men in \( x \) days can be expressed as:
\[ W = 2 \text{ men} \times x \text{ days} \]
This means that the work done by 2 men in \( x \) days is \( 2x \) man-days.

Similarly, the work done by \( y \) women in 3 days can be expressed as:
\[ W = y \text{ women} \times 3 \text{ days} \]
This means that the work done by \( y \) women in 3 days is \( 3y \) woman-days.

### Step 3: Set the work equations equal to each other
Since both expressions represent the same total work \( W \), we can set them equal:
\[ 2x = 3y \]

### Step 4: Find the work done by one man and one woman
To find the work done by one man in one day, we can express it as:
\[ \text{Work done by 1 man in 1 day} = \frac{W}{2x} = \frac{1}{2x} \text{ (since 2 men complete the work in x days)} \]

For one woman, the work done in one day is:
\[ \text{Work done by 1 woman in 1 day} = \frac{W}{3y} = \frac{1}{3y} \text{ (since y women complete the work in 3 days)} \]

### Step 5: Calculate the ratio of work done by one man to one woman
Now, we need to find the ratio of the work done by one man to the work done by one woman:
\[ \text{Ratio of work done by 1 man to 1 woman} = \frac{\frac{1}{2x}}{\frac{1}{3y}} = \frac{3y}{2x} \]

### Final Result
Thus, the ratio of the work done by 1 man to the work done by 1 woman is:
\[ \frac{3y}{2x} \]