IAS 2020 — CSAT Maths

Correct Option (3)

The problem states that 40% of men and 30% of women are married. Given the conditions of monogamy (no man marries more than one woman and no woman marries more than one man) and the absence of widows and widowers, the total number of married men must be equal to the total number of married women.

Let M represent the total number of men and W represent the total number of women in the city's adult population.

• Number of married men = 0.40M
• Number of married women = 0.30W

Equating the number of married individuals:

0.40M = 0.30W

This simplifies to 4M = 3W, or M = $\frac{3}{4}$43​W.

The total adult population is the sum of men and women:

Total Population = M + W = $\frac{3}{4}$43​W + W = $\frac{7}{4}$47​W

The total number of married individuals in the city is the sum of married men and married women. Since the number of married men equals the number of married women, we can express this as:

Total Married Individuals = 0.30W + 0.30W = 0.60W

To find the percentage of the married adult population, we divide the total married individuals by the total adult population and multiply by 100:

Percentage Married = $\left( \frac{\text{Total Married Individuals}}{\text{Total Population}} \right) \times 100$(Total PopulationTotal Married Individuals​)×100

Percentage Married = $\left( \frac{0.60\text{W}}{\frac{7}{4}\text{W}} \right) \times 100$(47​W0.60W​)×100

Percentage Married = $\left( \frac{0.60}{\frac{7}{4}} \right) \times 100$(47​0.60​)×100

Percentage Married = $\left( \frac{6}{10} \times \frac{4}{7} \right) \times 100$(106​×74​)×100

Percentage Married = $\left( \frac{24}{70} \right) \times 100$(7024​)×100

Percentage Married = $\frac{240}{7}\%$7240​%

Percentage Married = $34\frac{2}{7}\%$3472​%

Incorrect Options:

Options 1, 2, and 4 are incorrect. These values do not result from the accurate application of the given conditions and the derived mathematical relationships. Any calculation leading to these options would involve an error in setting up the initial equations or in the subsequent arithmetic operations for determining the proportion of the married population.