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

We break down this word problem step by step. Word problems can seem tricky, but once we identify what we know and what we need to find, they become much clearer.

What We Know:

Meena initially scores 40%

After review, her score increases by 50%, but she still fails by 35 marks

If her post-review score increases by another 20%, she gets 7 marks more than passing

We need to find the percentage required to pass

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We say the total marks for the examination = $x$

Meena's initial score = 40% of $x$ = $0.4x$

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When something increases by 50%, we multiply by 1.5 (since 100% + 50% = 150% = 1.5)

Meena's post-review score = $0.4x \times 1.5 = 0.6x$

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Since she fails by 35 marks with a score of $0.6x$, this means:

Passing marks = $0.6x + 35$

Think of it this way: If you need 35 more marks to pass, then passing marks = your current score + 35

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If her post-review score $(0.6x)$ increases by 20%:

New score = $0.6x \times 1.2 = 0.72x$

This new score is 7 marks more than the passing marks:

Passing marks = $0.72x - 7$

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Both expressions represent the same thing - the passing marks! So we can set them equal:

$0.6x + 35 = 0.72x - 7$

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$0.6x + 35 = 0.72x - 7$

$35 + 7 = 0.72x - 0.6x$

$42 = 0.12x$

$x = 350$

So the total marks = 350

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Passing marks = $0.6x + 35 = 0.6(350) + 35 = 210 + 35 = 245$

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Percentage needed to pass = $\frac{245}{350} \times 100 = 70\%$

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Answer: 70%

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Key Takeaway for Future Problems:

When dealing with percentage increase problems:

"Increased by 50%" means multiply by 1.5

"Increased by 20%" means multiply by 1.2

Set up equations by carefully reading what each scenario tells you about the same unknown value!