In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?

Correct Answer: The correct option is $34\frac{2}{7}\%$.

Step-by-Step Explanation:

Step 1: Understand the given conditions

Let $M$ represent the total number of adult men in the city, and $W$ represent the total number of adult women.

We are given that:

• $40\%$ of adult men are married.

• $30\%$ of adult women are married.

Since marriage is strictly monogamous and there are no widows or widowers, the total number of married men must equal the total number of married women.

Step 2: Relate the male and female populations

Equating the number of married men to the number of married women:

$40\%\text{ of }M=30\%\text{ of }W$

$\frac{40}{100}M=\frac{30}{100}W$

$4M=3W\Rightarrow W=\frac{4}{3}M$

Step 3: Calculate the total adult population and married population

1. Total adult population:

$\text{Total Population}=M+W=M+\frac{4}{3}M=\frac{7}{3}M$

2. Total married population:

Since the number of married women equals the number of married men ($0.40M$):

$\text{Total Married Population}=0.40M+0.40M=0.80M=\frac{4}{5}M$

Step 4: Find the percentage of the married adult population

The percentage of the total adult population that is married is given by:

$\text{Percentage}=\left(\frac{\text{Total Married Population}}{\text{Total Adult Population}}\right)\times 100$

Substituting the values:

$\text{Percentage}=\left(\frac{\frac{4}{5}M}{\frac{7}{3}M}\right)\times 100$

$=\frac{4}{5}\times \frac{3}{7}\times 100=\frac{12}{35}\times 100$

$=\frac{240}{7}\%=34\frac{2}{7}\%$

Thus, $34\frac{2}{7}\%$ of the adult population is married.