Of the adult population in a certain village 42% of men and 24% of women are married. Assuming that no man, marries more than one woman and vice versa, the percentage of total population of adult who are unmarried is?

Options

A. `69.45%`
B. `69.55%`
C. `68.75%`
D. `68.95%`

Answer

To solve the problem, we need to find the percentage of the total adult population in the village that is unmarried, given that 42% of men and 24% of women are married.

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of men in the village be \( M \) and the number of women be \( W \).

2. **Calculate Married Men and Women**:
- The number of married men = \( 0.42M \) (42% of men)
- The number of married women = \( 0.24W \) (24% of women)

3. **Establish Relationship Between Married Men and Women**:
Since each married man is married to one woman and vice versa, we can set the number of married men equal to the number of married women:
\[ 0.42M = 0.24W \]

4. **Find the Ratio of Men to Women**:
Rearranging the equation gives us:
\[ \frac{M}{W} = \frac{0.24}{0.42} = \frac{24}{42} = \frac{4}{7} \]
This means for every 4 men, there are 7 women.

5. **Express Total Population**:
Let’s assume \( M = 4x \) and \( W = 7x \) for some integer \( x \). The total adult population \( P \) is:
\[ P = M + W = 4x + 7x = 11x \]

6. **Calculate Unmarried Men and Women**:
- Unmarried men = \( M - \text{married men} = 4x - 0.42(4x) = 4x(1 - 0.42) = 4x(0.58) = 2.32x \)
- Unmarried women = \( W - \text{married women} = 7x - 0.24(7x) = 7x(1 - 0.24) = 7x(0.76) = 5.32x \)

7. **Total Unmarried Population**:
The total unmarried population is:
\[ \text{Total unmarried} = \text{Unmarried men} + \text{Unmarried women} = 2.32x + 5.32x = 7.64x \]

8. **Calculate Percentage of Unmarried Population**:
The percentage of the total population that is unmarried is given by:
\[ \text{Percentage of unmarried} = \left( \frac{\text{Total unmarried}}{P} \right) \times 100 = \left( \frac{7.64x}{11x} \right) \times 100 \]
Simplifying this gives:
\[ = \left( \frac{7.64}{11} \right) \times 100 \approx 69.45\% \]

### Final Answer:
The percentage of the total adult population who are unmarried is approximately **69.45%**.