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Data regarding the number of boys and girls in both colleges is as follows: - The average number of girls in St. Xavier College and Vijaya College is 210. - The total number of boys in both colleges is 810. - The number of girls is \(\tfrac{2}{3}\) of the number of boys in St. Xavier College. - The number of girls is \(\tfrac{2}{5}\) of the number of boys in Vijaya College. Find the difference between the total number of students in Vijaya College and the total number of students in St. Xavier College.

1. 15
2. 20
3. 25
4. 30

Correct answer: 30

Solution

Let girls in St. Xavier and Vijaya be \(G_1\) and \(G_2\). Since their average is 210, \(G_1+G_2=420\). Also, \(G_1=\tfrac{2}{3}B_1\Rightarrow B_1=\tfrac{3}{2}G_1\) and \(G_2=\tfrac{2}{5}B_2\Rightarrow B_2=\tfrac{5}{2}G_2\), with \(B_1+B_2=810\). Solving gives \(G_1=180, G_2=240\), so totals are 450 and 570; the difference is 30.

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