GATE 2024 MN – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

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Correct answer: (B) 200

Explanation

Let g be the common number of girls. Then class VIII has 450−g boys and class IX has 360−g boys. The reversed ratios give
$$\frac{g}{450-g}=\frac{360-g}{g}.$$
Cross-multiplying yields g²=162000−810g+g², so g=200.

Check: class VIII has 200 girls and 250 boys, ratio 4:5; class IX has 160 boys and 200 girls, also 4:5. The totals are 450 and 360 as required. Answer **B**.

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