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 400 and 300, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is A. 150 B. 200 C. 250 D. 175

GATE 2024 · General Aptitude · Ratio Proportion · medium

Answer: The number of girls in each class is 200. Answer: B.

1. Set up variables using equal girl counts: Number of girls in VIII = G, boys in VIII = 400-G. Girls in IX = G, boys in IX = 300-G.
2. Apply the cross-ratio condition: G^2 = (400 - G)(300 - G) = 120000 - 700G + G^2
3. Solve the linear equation: After cancellation: 0 = 120000 - 700G => G = 120000/600 = 200