If population of women in a village is 90% of population of men. what is the population of men as a percentage of population of women?

Options

A. 1
B. 10.5
C. 10.8
D. 11.1

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the population of men in the village be represented as \( M \) and the population of women as \( W \).

### Step 2: Establish the Relationship
According to the problem, the population of women is 90% of the population of men. This can be expressed mathematically as:
\[ W = 0.9M \]

### Step 3: Express Men in Terms of Women
To find the population of men as a percentage of the population of women, we need to express \( M \) in terms of \( W \). From the equation \( W = 0.9M \), we can rearrange it to find \( M \):
\[ M = \frac{W}{0.9} \]

### Step 4: Calculate the Percentage of Men with Respect to Women
Now, we want to find \( M \) as a percentage of \( W \). The formula for percentage is:
\[ \text{Percentage} = \left( \frac{M}{W} \right) \times 100 \]
Substituting \( M \) from Step 3 into this formula gives:
\[ \text{Percentage} = \left( \frac{\frac{W}{0.9}}{W} \right) \times 100 \]

### Step 5: Simplify the Expression
The \( W \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{1}{0.9} \right) \times 100 \]

### Step 6: Calculate the Final Value
Now, calculate \( \frac{1}{0.9} \):
\[ \frac{1}{0.9} = \frac{10}{9} \approx 1.1111 \]
Thus,
\[ \text{Percentage} = 1.1111 \times 100 = 111.11\% \]

### Conclusion
The population of men as a percentage of the population of women is approximately **111.11%**.

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