What is the difference between the total number of students in Colleges B and…

Concept

If a category forms p% of a total T, the remaining categories form (100 − p)% of T.

Therefore, if the remaining-category count is R, then T = R ÷ (1 − p/100), and the category count is pT/100.

Application

1. For College B, Chess and Squash together are 65% of the total because Carrom is 35%. Hence, total students in B = 1170 ÷ 0.65 = 1800.

2. For College C, Chess and Squash together are 60% of the total because Carrom is 40%. Hence, total students in C = 1260 ÷ 0.60 = 2100.

3. The combined total for Colleges B and C is 1800 + 2100 = 3900.

4. For College A, Chess and Squash together are 70% of the total because Carrom is 30%. Thus, total students in A = 2100 ÷ 0.70 = 3000, so students learning Carrom = 30% of 3000 = 900.

5. The required difference is 3900 − 900 = 3000 students.

Cross-check

All reconstructed totals agree with the table; therefore, the required difference is 3000 students.