In a city `45%` of the men are married and `25%` of women are married. Considering that nobody is married more than once. What percent of population is married?

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Given Information
We know that:
- 45% of men are married.
- 25% of women are married.
- No one is married more than once.

### Step 2: Set Up Ratios
Since the percentage of married men and women must be equal (because each married man corresponds to a married woman), we can set up the following equation:
- Let the number of men be represented as \( M \) and the number of women as \( W \).
- According to the problem, we can equate the married men to married women:
\[ 0.45M = 0.25W \]

### Step 3: Simplify the Equation
To find the ratio of men to women, we can rearrange the equation:
\[ \frac{M}{W} = \frac{0.25}{0.45} \]
This simplifies to:
\[ \frac{M}{W} = \frac{25}{45} = \frac{5}{9} \]
This means for every 5 men, there are 9 women.

### Step 4: Assign Values to Men and Women
Let’s assign values based on the ratio:
- Let the number of men be \( 5k \) and the number of women be \( 9k \), where \( k \) is a common factor.

### Step 5: Calculate the Number of Married Individuals
Now we can calculate the number of married men and women:
- Married men:
\[ \text{Married Men} = 0.45 \times 5k = \frac{225k}{100} = 2.25k \]
- Married women:
\[ \text{Married Women} = 0.25 \times 9k = \frac{225k}{100} = 2.25k \]

### Step 6: Total Married Population
The total number of married individuals (both men and women) is:
\[ \text{Total Married} = 2.25k + 2.25k = 4.5k \]

### Step 7: Calculate Total Population
The total population (men + women) is:
\[ \text{Total Population} = 5k + 9k = 14k \]

### Step 8: Calculate the Percentage of Married Population
To find the percentage of the population that is married, we use the formula:
\[ \text{Percentage Married} = \left( \frac{\text{Total Married}}{\text{Total Population}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Married} = \left( \frac{4.5k}{14k} \right) \times 100 \]
The \( k \) cancels out:
\[ \text{Percentage Married} = \left( \frac{4.5}{14} \right) \times 100 \approx 32.14\% \]

### Final Answer
Thus, the percentage of the population that is married is approximately **32.14%**.

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