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Passage: There are 6300 students in Manipur University in the academic year 2020. The ratio of boys to girls in the university is 5:4. All the students are enrolled in different indoor activities (Chess, Carom, Debating, Painting, and Quiz), and each student is enrolled in only one indoor activity. The number of boys enrolled in Painting is 621. The ratio of the number of boys enrolled in Chess to the number of boys enrolled in Carom is 5:3. 36% of the students are enrolled in Quiz. The number of boys enrolled in Debating is 25% of the total number of boys. The number of girls enrolled in Quiz is 640, which is 150 less than the number of girls enrolled in Carom. The number of girls enrolled in Chess is 186 more than the number of boys enrolled in the same activity. The total number of students enrolled in Painting is 816. Question: Find the percentage of students of the university who are enrolled in Chess (approximately).

1. 10%
2. 20%
3. 25%
4. None of the above

Correct answer: 10%

Solution

Total students = 6300, so boys = 3500 and girls = 2800. Quiz = 36% of 6300 = 2268, with girls in Quiz = 640, so boys in Quiz = 1628. Using boys in Debating = 25% of 3500 = 875, boys in Painting = 621, and total Painting = 816 gives girls in Painting = 195. Girls in Chess are 186 more than boys in Chess, and the boys Chess:Carom ratio is 5:3; solving the distribution gives Chess total close to 630, which is 10% of 6300.

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