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Meena scores $40\%$ in an examination and after review, even though her score is increased by $50\%$, she fails by $35$ marks. If her post-review score is increased by $20\%$, she will have $7$ marks more than the passing score. The percentage score needed for passing the examination is

- $70$
- $60$
- $75$
- $80$

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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 $: \text{A}$

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 $: \text{A}$