$\frac{5}{9}$ part of the population in a village are males. If $30\%$ of the males are married, the percentage of unmarried females in the total population is

### Concept & Logic This problem requires assuming a convenient base population to simplify fraction and percentage calculations. Additionally, it relies on an implicit logical assumption standard in aptitude tests: in a closed population (like a village), a marriage involves one male and one female. Therefore, the number of married males exactly equals the number of married females. ### Step-by-Step Solution * **Given:** Males = $\frac{5}{9}$ of the total population. Married males = $30\%$ of total males. * **Calculation / Deduction:** Let the total population of the village be $900$ (a multiple of $9$ and $100$ makes the math extremely clean). Total males = $\frac{5}{9} \times 900 = 500$. Total females = $900 - 500 = 400$. Calculate married males: Married males = $30\%$ of $500 = \frac{30}{100} \times 500 = 150$. Apply the logic of pairs: Since $150$ males are married, they must be married to $150$ females. Therefore, the number of married females = $150$. Find unmarried females: Unmarried females = Total females - Married females Unmarried females = $400 - 150 = 250$. Calculate the required percentage: Percentage of unmarried females in the total population = $\left( \frac{250}{900} \right) \times 100\%$ $= \frac{250}{9}\% = 27\frac{7}{9}\%$. ### Exam Strategy & Shortcut Whenever you see a fraction like $\frac{5}{9}$ alongside percentages, immediately assume a base that contains both $9$ and $100$ as factors. Using $900$ turns the entire problem into simple mental arithmetic: Males = $500$, Females = $400$. $30\%$ of $500 = 150$. Married females = $150$. Unmarried females = $250$. $\frac{250}{900} = \frac{25}{90} = \frac{5}{18}$. To get the percentage, $\frac{250}{9} = 27.77\%$, which matches $27\frac{7}{9}\%$. ### Common Pitfall The single most common mistake is overlooking the implicit rule that "Number of Married Males = Number of Married Females". Students often get stuck after calculating $150$ married males because they feel they don't have enough information to find the female marital status. ### Final Answer **Therefore, the correct answer is $27\frac{7}{9}\%$.**