Question

In a fraction, the numerator is increased by $25\%$ and the denominator is diminished by $10\%$. The new fraction obtained is $\frac{5}{9}$. The original fraction is

• A. $\frac{2}{5}$
• B. $\frac{3}{4}$
• C. $\frac{4}{5}$
• D. $\frac{1}{9}$

Answer 1

The correct option is A $\frac{2}{5}$

Let the fraction be $\frac{a}{b}$.

If the numerator is increased by $25\%$, then $a^{\prime }=1.25a$

If the denominator is decreased by $10\%$, then $b^{\prime }=0.9b$

The new fraction is $\frac{5}{9}$.

Equating $\frac{a^{\prime }}{b^{\prime }}$ to $\frac{5}{9}$, we get

$\frac{a^{\prime }}{b^{\prime }}=\frac{5}{9}\Rightarrow \frac{1.25a}{0.9b}=\frac{5}{9}\Rightarrow \frac{a}{b}=\frac{5\times 0.9}{9\times 1.25}=\frac{4}{10}=\frac{2}{5}$

The original fraction $\frac{a}{b}$ is $\frac{2}{5}.$