Question

In Anirudhville, $60\%$ of the female population comprised of married females. Of these, $\frac{3}{4}$ the number had been married for more than $5$ years. Of the number of women who had been married for more than $5$ years $\frac{3}{5}$ were married for less than $10$ years. If $108$ women had been married for $10$ years or more, how many females did Anirudhville have?

• A. $100$
• B. $200$
• C. $400$
• D. $600$

Answer 1

Answer: (D)

$600$

Let $x$ be the total female population

given:

$60\%ofx$ are married $=\frac{3x}{5}$

of these $\frac{3x}{5}$ , ${\left(\frac{3}{4}\right)}^{th}$ are married $>5$ years

$⟹\frac{3}{4}$ of $\frac{3x}{5}=\frac{9x}{20}$

of these $\frac{9x}{20}$ , ${\left(\frac{3}{5}\right)}^{th}$ are married $<10$ years

$⟹\frac{3}{5}$ of $\frac{9x}{20}=\frac{27x}{100}$

$\therefore$ women who are married $>10$ years

$⟹\frac{2}{5}$ of $\frac{9x}{20}=\frac{18x}{100}$

given that $108=\frac{18x}{100}$

$\therefore x=600$ , which is the total female population.