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Question

In a quarterly examination, a student secured $$30$$% marks are failed by $$12$$ marks. In the same examination, another student secured $$40$$% marks and got $$28$$ marks more than the minimum marks to pass. Find the pass percentage.


A
24%
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B
28%
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C
25%
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D
33%
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Solution

The correct option is D $$33$$%
Let the maximum marks be $$x$$.

According to question,
$$30$$% of $$x + 12 = 40$$% of $$x - 28$$
$$\Rightarrow \dfrac {30}{100}x + 12 = \dfrac {40}{100}x - 28 $$

$$\Rightarrow \dfrac {10}{100}x = 40\Rightarrow x = 400$$
Passing marks $$= \dfrac {30}{100}\times 400 + 12 = 132$$
Hence, pass percentage $$= \dfrac {132}{400}\times 100 = 33$$%.

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