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In an examination 50% of students passed in physics, 37.5% of students passed in chemistry, and 12.5% of students passed in both. If in that exam the no. of girls is equal to the no. of failed students and 25% of the failed students are girls, which is 20, then find what percent of boys got fail?

In an examination 50% of students passed in physics, 37.5% of students passed in chemistry, and 12.5% of students passed in both. If in that exam the no. of girls is equal to the no. of failed students and 25% of the failed students are girls, which is 20, then find what percent of boys got fail? Correct Answer 25%

Given: 50% students passed in physics, 37.5% students passed in chemistry and 12.5% students passed in both.

25% of the failed students are girls = 20

Concept: Ven diagram.

Solution:

Let the no. of students in the exam = x

So, the no. of passed students = (50 + 37.5 – 12.5)% of x

⇒ x × (75/100) = 3x/4

And, the no. of failed students = (100 – 75)% of x = x × (25/100) = x/4

The no. of failed girls = (x/4) × (25/100) = 20

⇒ x = 320

The no. of failed boys = – 20 = 60

The total no. of boys = 320 – the no. of girls = 320 – (320/4) = 240

Required percentage = (60/240) × 100 = 25%

∴ Percentage of boys who got fail is 25%.

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