Men constitute five-ninth of the population of a town. 60% of the men in the town are married to women of the same town. What is the percentage of the unmarried women in the total population of the town?

Let's break down the problem step by step.

### Step 1: Define the population
Let the total population of the town be \( P \).

### Step 2: Calculate the number of men
Men constitute \( \frac{5}{9} \) of the population. So, the number of men in the town is:
\[
\text{Number of men} = \frac{5}{9} \times P
\]

### Step 3: Calculate the number of women
The rest of the population is women. Since \( \frac{5}{9} \) of the population are men, the fraction of the population that are women is:
\[
\text{Fraction of women} = 1 - \frac{5}{9} = \frac{4}{9}
\]
Thus, the number of women in the town is:
\[
\text{Number of women} = \frac{4}{9} \times P
\]

### Step 4: Calculate the number of married men
60% of the men are married. So, the number of married men is:
\[
\text{Number of married men} = 0.60 \times \frac{5}{9} \times P = \frac{3}{9} \times P = \frac{1}{3} \times P
\]

### Step 5: Assume married men are married to women of the same town
Since each married man is married to one woman, the number of married women is the same as the number of married men:
\[
\text{Number of married women} = \frac{1}{3} \times P
\]

### Step 6: Calculate the number of unmarried women
The number of unmarried women is:
\[
\text{Number of unmarried women} = \text{Total number of women} - \text{Number of married women}
\]
\[
\text{Number of unmarried women} = \frac{4}{9} \times P - \frac{1}{3} \times P
\]
To simplify this:
\[
\text{Number of unmarried women} = \frac{4}{9} \times P - \frac{3}{9} \times P = \frac{1}{9} \times P
\]

### Step 7: Calculate the percentage of unmarried women in the total population
The percentage of unmarried women in the total population is:
\[
\text{Percentage of unmarried women} = \left(\frac{\text{Number of unmarried women}}{P}\right) \times 100\%
\]
Substitute the value from Step 6:
\[
\text{Percentage of unmarried women} = \left(\frac{\frac{1}{9} \times P}{P}\right) \times 100\%
\]
\[
\text{Percentage of unmarried women} = \frac{1}{9} \times 100\% = \frac{100\%}{9} \approx 11.11\%
\]

Thus, the percentage of unmarried women in the total population of the town is **11.11%**.

Would you like further details or have any questions?

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Here are five related questions to explore further:
1. What percentage of the total population are married men?
2. If 10% of the total population moves out of the town, how does it affect the percentage of unmarried women?
3. How would the percentage of unmarried women change if 70% of the men were married?
4. If the population of the town increases by 20%, what will be the new number of unmarried women?
5. How does the percentage of married men compare to the percentage of married women?

**Tip**: When working with fractions and percentages, converting everything to the same base (like total population) makes comparisons and calculations much easier.

Learn how to calculate the percentage of unmarried women in a town's population using fractions and percentages. This problem involves understanding population distribution, fractions, and percentage calculations. Suitable for high school students.

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