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

1. $2/5$
2. $5/9$
3. $3/5$
4. None of the above

Let original fraction is $\frac{a}{b}$,where $a$ is numerator and $b$ is denominator.

$\Rightarrow \frac{125\% *a}{90\%*b}=\frac{5}{9}$

$\Rightarrow \frac{\left ( \frac{125}{100}*a \right )}{\left(\frac{90}{100}*b \right )}=\frac{5}{9}$

$\Rightarrow \frac{a}{b}=\frac{5*90}{9*125}$

$\Rightarrow \frac{a}{b}=\frac{2}{5}$

Option $(A)$ is correct.

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