Question

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:

• A. \( 150 \)
• B. \( 200 \)
• C. \( 250 \)
• D. \( 175 \)

Hint:

When dealing with ratio problems, carefully write the given conditions as equations and solve step by step.

Answer 1

The Correct Option is B

Step 1: Let the number of girls in each class be \( x \). In class VIII, the number of boys is \( 450 - x \). In class IX, the number of boys is \( 360 - x \). Step 2: Ratio condition. The ratio of girls to boys in class VIII is the reciprocal of the ratio in class IX: \[ \frac{x}{450 - x} = \frac{360 - x}{x}. \] Cross-multiplying: \[ x^2 = (450 - x)(360 - x). \] Step 3: Solving the equation. Solving \( x = 200 \). Step 4: Conclusion. The number of girls in each class is \( {(2) 200} \).