The following table shows the percentage (%) distribution of students studying…
2022
The following table shows the percentage (%) distribution of students studying in six classes A-F of a school and shows the ratio of boys to girls among them. Number of students studying in all six classes together is 600.
Class-wise distribution of students
Class | % Students | Ratio Boys : Girls |
|---|---|---|
A | 20% | 3 : 2 |
B | 12% | 3 : 1 |
C | 16% | 5 : 3 |
D | 15% | 8 : 7 |
E | 21% | 4 : 3 |
F | 16% | 1 : 1 |
The average of the number of girls studying in all six classes, A-F, is
Answer: A. 41 — ConceptFor a group split in the ratio boys : girls = b : g, the girls’ share is g/(b + g) of that group. For each class, first use its percentage to find the…
- A.
41
- B.
42
- C.
43
- D.
44
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
For a group split in the ratio boys : girls = b : g, the girls’ share is g/(b + g) of that group.
For each class, first use its percentage to find the class total, then apply the girls’ share. The arithmetic mean is the sum of the six girl counts divided by 6.
Application
Class A has 20% of 600 = 120 students; girls = 120 × 2/5 = 48.
Class B has 12% of 600 = 72 students; girls = 72 × 1/4 = 18.
Class C has 16% of 600 = 96 students; girls = 96 × 3/8 = 36.
Class D has 15% of 600 = 90 students; girls = 90 × 7/15 = 42.
Class E has 21% of 600 = 126 students; girls = 126 × 3/7 = 54.
Class F has 16% of 600 = 96 students; girls = 96 × 1/2 = 48.
Total girls = 48 + 18 + 36 + 42 + 54 + 48 = 246.
Average number of girls = 246/6 = 41.
Cross-check
The weighted fraction of girls among all 600 students is 20% × 2/5 + 12% × 1/4 + 16% × 3/8 + 15% × 7/15 + 21% × 3/7 + 16% × 1/2 = 41%.
Therefore, 600 × 41% = 246 girls, and 246/6 = 41 girls per class.