Express $0.\overline{75}$ as rational number.

A. $\frac{75}{99}$

B. $\frac{26}{33}$

C.$\frac{3}{4}$

D. None of these

The correct option is A: $\frac{75}{99}$

Let $x=0.\overline{75}=0.75757575\dots \left(i\right)$

Multiply both sides by $100$; we have

$100x=75.75757575\dots \left(ii\right)$

Subtract equation $\left(i\right)$ from $\left(ii\right)$; we get

$100x-x=75.75757575\dots -0.75757575\dots$

$99x=75$

$x=\frac{75}{99}$

Hence, option A is the correct answer.