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GATE 2024 CE (CE2) – 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

  1. 150
  2. 200
  3. 250
  4. 175

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Correct answer: (B) 200

Explanation

Let $g$ be the number of girls in each class. Then class VIII has $450 - g$ boys and class IX has $360 - g$ boys. The condition is $\frac{g}{450 - g} = \frac{360 - g}{g}$, so $g^2 = (450 - g)(360 - g) = 162000 - 810g + g^2$. This gives $g = \frac{162000}{810} = 200$.