What is the ratio of the number of students learning Chess in Colleges A and B…

Concept

If the sum of two quantities is S and their positive difference is d, the larger quantity is (S + d)/2. If a third group is p% of the total, the other groups together form (100 − p)% of that total. A ratio is simplified by dividing both terms by their greatest common divisor.

Application

1. For College A, Chess learners = (2100 + 300)/2 = 1200. For College B, Chess learners = (1170 + 30)/2 = 600. Therefore, Colleges A and B together have 1200 + 600 = 1800 Chess learners.

2. In College D, Carrom learners are 25% of all students, so Chess and Squash learners together are 75%. Hence the total number of students is 1800/0.75 = 2400, and Carrom learners = 25% of 2400 = 600.

3. The required ratio is 1800 : 600. Dividing both terms by 600 gives 3 : 1.

Cross-check and contrast

College D has 600 Carrom learners and 1800 Chess-plus-Squash learners; 600 is 25% and 1800 is 75% of 2400, so the reconstruction matches the table.

• 2 : 5 means the first quantity is 0.4 times the second.

• 4 : 3 means the first quantity is about 1.33 times the second.

• 4 : 5 means the first quantity is 0.8 times the second.

Therefore, the required ratio is 3 : 1.