In a group of persons, 70% of the persons are male and 30% of the persons are married. If two-sevenths of the males are married, what fraction of the females is single?

Correct Option (4)

To determine the fraction of females who are single, we can assume a total population for calculation purposes. Let the total number of persons in the group be 100 units.

• Number of males = 70% of 100 = 70 units.
• Number of females = 30% of 100 = 30 units.
• Total number of married persons = 30% of 100 = 30 units.

It is given that two-sevenths of the males are married.

• Number of married males = $\frac{2}{7}\times 70=20$ units.

The total number of married persons is 30 units. Since 20 units are married males, the remaining married individuals must be females.

• Number of married females = Total married persons - Married males = $30-20=10$ units.

To find the number of single females, subtract the married females from the total number of females.

• Number of single females = Total females - Married females = $30-10=20$ units.

The question asks for the fraction of females that is single. This is calculated as the ratio of single females to the total number of females.

• Fraction of females that is single = $\frac{\text{Number of single females}}{\text{Total number of females}}=\frac{20}{30}=\frac{2}{3}$.

Incorrect Options:

Options 1 (2/7), 2 (1/3), and 3 (3/7) are incorrect as they do not align with the derived fraction of single females, which is $\frac{2}{3}$.