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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.

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

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

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

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

Option $(A)$ is correct.