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
150
200
250
175
ANSWER
Each class has 200 girls. Option (B).
Official answer: BSource: Official answer key, GATE 2024 IN (IISc Bengaluru)
Let be the number of girls in each class. The question says the number is the same in class VIII and class IX.
Boys = total minus girls. Class VIII has boys and class IX has boys.
The question says (girls : boys in VIII) = (boys : girls in IX), so
Cross-multiply:
The terms cancel and a linear equation is left: , so .
Check: class VIII has 200 girls and boys, so girls : boys . Class IX has boys and 200 girls, so boys : girls . The two ratios are equal, so the answer is (B) 200.
KEY IDEA
Use one variable for the girls, since their number is the same in both classes. Write each class's boys as total minus girls and set the two ratios equal. Because the ratios are reversed (girls : boys against boys : girls), the terms cancel when you cross-multiply, and what is left is a linear equation.
WATCH OUT FOR
Reading both ratios as girls : boys and writing . That has no positive solution, because it forces . Another slip is expanding with the wrong sign on the term. Testing the options is a fast check: with 200 girls, class VIII is and class IX is , and both are .
From the GATE 2024 IN paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes
