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In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is _______

Let $100x$ be the total number of student in a class.

The girls are in a class $= 60\% = 100x \times \frac{60}{100} = 60x$

And, the boys are in a class $= 100\% – 60\% = 40\% = 100x \times \frac{40}{100} = 40x$

According to the question :

There are $30$ more girls than boys.

$60x = 40x + 30$

$\Rightarrow 60x – 40x = 30$

$\Rightarrow 20x = 30$

$\Rightarrow \boxed{x = \frac{3}{2}}$

The number of student in a class $= 100x = 100 \times \frac{3}{2} = 150$

Therefore,

• The total number of girls in a class $= 60x = 60 \times \frac{3}{2} = 90$
• The total number of boys in a class $= 40x = 40 \times \frac{3}{2} = 60$

If $68\%$ of the students, including $30$ boys pass an examination.

Then, total number of students who passes in the exam (including $30$ boys) $= 150 \times \frac{68}{100} = 102$

Let $k$ be the number of girls who passed in the exam.

$30 \; \text{(Boys)} + k \; \text{(Girls)} = 102$

$\Rightarrow k = 102 – 30$

$\Rightarrow k = 72$

The total number of girls in a class $= 90$

Therefore,

• Number of girls who passed in the exam $= 72$
• Number of girls who failed in the exam $= 90 – 72 = 18$

$\therefore$ The percentage of the girls who failed in the exam$= \frac{18}{90} \times 100 = 20\%.$

Correct Answer $: 20$

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