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 = 72×70=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 = Total number of femalesNumber of single females=3020=32.
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 32.