Arithmetic

Percentages

Medium

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

Entered answer:

✅ Correct Answer: 20

Let's say there are $x$ boys in the class.

Since there are 30 more girls than boys:

Girls = $x + 30$

Therefore:

Total students = $x + (x + 30) = 2x + 30$

The key insight is that 60% of total students are girls.

This means:

60% of total students = Number of girls

Writing this as an equation:

$(2x + 30) \times 0.6 = x + 30$

The left side gives us 60% of all students, and the right side is the actual number of girls. These must be equal.

$(2x + 30) \times 0.6 = x + 30$

$1.2x + 18 = x + 30$

$1.2x - x = 30 - 18$

$0.2x = 12$

$x = 60$

So we have:

Boys = 60

Girls = $60 + 30 = 90$

Total students = 150

From the problem:

68% of students passed = $68\% \times 150 = 102$ students

30 boys passed (given)

Therefore:

Girls who passed = $102 - 30 = 72$

Girls who failed = Total girls - Girls who passed

Girls who failed = $90 - 72 = 18$

Percentage of girls who don't pass = $\tfrac{\text{Girls who failed}}{\text{Total girls}} \times 100$

$= \tfrac{18}{90} \times 100 = 20\%$

When dealing with percentage problems involving groups, we always convert percentages to actual numbers first. This makes the calculations much clearer and helps avoid common mistakes.

Answer: 20

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In a class, 60%60\%60% of the students are girls and the rest are boys. There are 303030 more girls than boys. If 68%68\%68% of the students, including 303030 boys, pass an examination, the percentage of the girls who do not pass is

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CAT Past Year Questions (Topic-Wise)

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