Q) 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.

Solution:
Explanation: Given: - Number of girls in both classes is \( X \). - Total students in 8th class = 450. - Total students in 9th class = 360. The ratio condition is: \[\frac{X}{450 - X} = \frac{360 - X}{X}\] Cross-multiplying and solving: \[X^2 = (450 - X)(360 - X)\] Expanding and solving the quadratic equation: \[X^2 = 162000 - 450X - 360X + X^2\] \[0 = 162000 - 810X\] \[X = \frac{162000}{810} = 200\] So, the number of girls in each class is 200.