In a village, 5/9 of the population are females and 30% of these females are married. What percentage of the total male population in the village are unmarried?

Introduction / Context:
This problem mixes ratios and percentages in a population setting. The key idea is to interpret the fractions of females and males, then use the percentage of married females to infer how many males are married, assuming each married female is paired with one married male. Finally, we compute the share of unmarried males as a percentage of the total male population.

Given Data / Assumptions:

Females constitute 5/9 of the total population.

Therefore males constitute the remaining 4/9 of the total population.

30% of the females are married.

Each married female is married to exactly one male, and there are no polygamous or other special cases.

We need the percentage of unmarried males in the total male population.

Concept / Approach:
It is convenient to assume the total population is 9 units so that 5 units are females and 4 units are males. Then 30% of the females are married, giving a fixed number of married females. Under the assumption of monogamous couples, the number of married males must equal the number of married females. Subtracting married males from the total male population gives unmarried males. Finally, we convert that number into a percentage of all males.

Step-by-Step Solution:
Step 1: Assume total population = 9x for some positive x.Step 2: Females = (5 / 9) * 9x = 5x and males = (4 / 9) * 9x = 4x.Step 3: 30% of females are married.Married females = 30% of 5x = (30 / 100) * 5x = 1.5x.Step 4: Under one to one marriage assumption, married males = 1.5x.Step 5: Unmarried males = total males − married males = 4x − 1.5x = 2.5x.Step 6: Percentage of unmarried males among total males = (2.5x / 4x) * 100.The x cancels out giving (2.5 / 4) * 100 = 0.625 * 100 = 62.5%.

Verification / Alternative check:
Take a concrete example: let x = 2 so that total population is 18. Then females = 10, males = 8. Married females = 30% of 10 = 3, married males = 3, so unmarried males = 8 − 3 = 5. Therefore the percentage of unmarried males = (5 / 8) * 100 = 62.5%, which matches the calculated result.

Why Other Options Are Wrong:
125% is impossible as a percentage of a group and clearly incorrect.
84.32% and 46.87% are random looking decimals that do not follow from the ratio calculations.
37.5% is the complement of 62.5% but would represent married males, not unmarried males, under the given data.

Common Pitfalls:
Students sometimes confuse percentage of total population with percentage of male population. Another mistake is to treat 5/9 and 4/9 as literal numbers instead of proportional values, or to ignore the assumption that each married female pairs with one male. Carefully defining a convenient total population like 9 or a multiple helps keep the arithmetic and logic straightforward.

Final Answer:
The percentage of unmarried males among the total male population is 62.5%.