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CAT 2019 Quant Question with Solution 3

Question:
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 number of girls and boys be 3x and 2x respectively.

Given,

3x-2x=30

Or x = 30. So the number of students = 3x+2x=5x =150.

Also, number of girls (3x) and boys (2x) = 90 and 60 respectively.

Number of students pass the exam = 68% of 150=102.
Number of girls pass the exam = 102-30 = 72 .

Therefore, number of girls who fail in the exam = 90-72=18

Hence, percentage of girls fail the exam = $\frac{18}{90}\times 100=20%$

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