Number systems — Maths STD 9 — Question

Let $\text{x}=0.\overline{3}$
i.e., $\text{x}=0.3333 \ ...(\text{i})​​$
$\Rightarrow10\text{x}=3.3333 \ ...(\text{ii})​​$
On subtracting $(i)$ and $(ii),$ we get
$9\text{x}=3$
$\Rightarrow\text{x}=\frac{3}{9}$
Let $\text{y}=0.\overline{4}$
i.e., $\text{y}=0.4444 \ ...(\text{i})​​$
$\Rightarrow10\text{y}=4.4444 \ ...(\text{ii})​​$
On subtracting $(i)$ and $(ii),$ we get
$9\text{y}=4$
$\Rightarrow\text{y}=\frac{4}{9}$
$\therefore0.\overline{3}+0.\overline{4}=\text{x}+\text{y}=\frac{\text{3}}{\text{9}}+\frac{\text{4}}{\text{9}}=\frac{\text{7}}{\text{9}}$
Hence, the correct answer is option $(b).$