$\frac{5}{9}$ 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
(a)20\%
(b)$27 \frac{7}{9} \%$
(c)40\%
(d)70\%
Answer
Answer (as printed): B
Explanation
Let total population $=x$. Then, number of males $=\frac{5}{9} x$. $$\text { Married males }=30 \% \text { of } \frac{5}{9} x=\left(\frac{30}{100} \times \frac{5}{9} x\right)=\frac{x}{6} .$$ Married females $=\frac{x}{6}$; Number of females $=\left(x-\frac{5}{9} x\right)=\frac{4 x}{9}$. Unmarried females $=\left(\frac{4 x}{9}-\frac{x}{6}\right)=\frac{5 x}{18}$. $$\text { ∴ } \quad \text { Required percentage }=\left(\frac{5 x}{18} \times \frac{1}{x} \times 100\right) \%=27 \frac{7}{9} \% .$$
Explanation as extracted from the printed page; notation may be imperfect.