In College B, the ratio of boys to girls is 5:4, and 30% of the girls learn…

Concept

When a population is partitioned by percentage, the complementary share is 100% minus the stated share. Dividing a known subgroup count by its share of the whole recovers the total population, after which a part-to-part ratio gives the sizes of its groups.

For two categories with known sum and difference, their individual counts can be found by simultaneous equations; here, the required boys count can instead be obtained by subtracting boys learning Carrom from total boys.

Application

1. For College B, 35% learn Carrom, so 65% learn Chess or Squash.

2. Therefore, total students in College B = 1,170 ÷ 0.65 = 1,800.

3. The ratio of boys to girls is 5:4, so there are 9 equal parts and each part represents 1,800 ÷ 9 = 200 students.

4. Number of boys = 5 × 200 = 1,000, and number of girls = 4 × 200 = 800.

5. Girls learning Carrom = 30% of 800 = 240.

6. Total students learning Carrom = 35% of 1,800 = 630, so boys learning Carrom = 630 − 240 = 390.

7. Boys learning Chess and Squash in total = 1,000 − 390 = 610.

Cross-check

The boys and girls total is 1,000 + 800 = 1,800. Their Carrom counts are 390 and 240, totaling 630, which is 35% of 1,800; the remaining 1,170 students match the table.

Hence, the number of boys learning Chess and Squash in total is 610.