The proportions of male students and vegetarian students in a school are given…

Concept

In a data-interpretation table where a whole population is split into named sub-groups, and only some sub-group percentages are given directly, the count for any missing sub-group is found by the residual method: convert every known percentage into an actual count, then subtract the known sub-group counts from the whole-population count to isolate the missing sub-group's count. Converting that residual count back to a percentage of its own sub-group's strength gives the missing percentage.

Step-by-step

1. Total students = 800; the Secondary Section = 80% of 800 = 640, so the remaining 800 - 640 = 160 students are split equally between Class 11 and Class 12, giving 160 / 2 = 80 students in each of Class 11 and Class 12.

2. Total vegetarian students in the school = 53% of 800 = 424.

3. Vegetarian students in the Secondary Section = 55% of 640 = 352.

4. Vegetarian students in Class 11 = 50% of 80 = 40.

5. Vegetarian students in Class 12 = school-wide vegetarian count minus the two known sub-group counts = 424 - 352 - 40 = 32.

6. Percentage of vegetarian students in Class 12 = (32 / 80) × 100 = 40%.

Cross-check

Adding the three sub-group vegetarian counts back together -- 352 (Secondary Section) + 40 (Class 11) + 32 (Class 12) = 424 -- reproduces the school-wide vegetarian total of 53% of 800, confirming the residual figure is correct.