Let $100x$ be the total marks in an examination.
Meena score $40\%$ in an examination $= 40\%$ of $100x = \frac{40}{100} \times 100x = 40x$
Her score is increased by $50\%$ after review $= 40x \times \frac{150}{100} = 60x\; \left[\text{She failed by 35 marks}\right]$
So, the passing marks of her $ = 60x+35 \quad \longrightarrow (1) $
Her post review score is increased by $20\% = 60x \times \frac{120}{100} = 72x$
After post review, she got $7$ marks more than the passing marks.
So, the passing marks of her $ = 72x-7 \quad \longrightarrow (2) $
Equate the equation $(1)$ and $(2),$ we get
$ 60x+35 = 72x-7 $
$ \Rightarrow 35+7 = 12x $
$ \Rightarrow 42 = 12x $
$\Rightarrow x = \frac{42}{12}$
$ \Rightarrow \boxed{x = \frac{7}{2}} $
Now, the total marks in an examination $ = 100x = 100 \times \frac {7}{2} = 350 $
And passing marks in a examination $ = 60x+35 = 60 \times \frac{7}{2} + 35 = 245 $
$\therefore$ The percentage score needed for passing the examination $ = \frac{245}{350} \times100 = 70\%.$
Correct Answer $: \text{A}$