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 difference between the number of boys and the number of girls in all the six classes A-F together, is
Answer: D. 108 — ConceptA percentage distribution converts the overall total into each class total: class total = overall total × percentage ÷ 100. For a class split in the…
- A.
102
- B.
114
- C.
106
- D.
108
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
A percentage distribution converts the overall total into each class total: class total = overall total × percentage ÷ 100.
For a class split in the ratio b:g, boys = class total × b ÷ (b + g), girls = class total × g ÷ (b + g), and the boy–girl difference is class total × |b − g| ÷ (b + g).
Application
Class A: 600 × 20% = 120 students; difference = 120 × (3 − 2) ÷ 5 = 24.
Class B: 600 × 12% = 72 students; difference = 72 × (3 − 1) ÷ 4 = 36.
Class C: 600 × 16% = 96 students; difference = 96 × (5 − 3) ÷ 8 = 24.
Class D: 600 × 15% = 90 students; difference = 90 × (8 − 7) ÷ 15 = 6.
Class E: 600 × 21% = 126 students; difference = 126 × (4 − 3) ÷ 7 = 18.
Class F: 600 × 16% = 96 students; difference = 96 × (1 − 1) ÷ 2 = 0.
Total difference = 24 + 36 + 24 + 6 + 18 + 0 = 108 students.
Cross-check
The class totals add to 120 + 72 + 96 + 90 + 126 + 96 = 600, matching the stated school total. Computing totals directly gives:
Class | Students | Boys | Girls | Difference |
|---|---|---|---|---|
A | 120 | 72 | 48 | 24 |
B | 72 | 54 | 18 | 36 |
C | 96 | 60 | 36 | 24 |
D | 90 | 48 | 42 | 6 |
E | 126 | 72 | 54 | 18 |
F | 96 | 48 | 48 | 0 |
Total | 600 | 354 | 246 | 108 |
The class totals add to 120 + 72 + 96 + 90 + 126 + 96 = 600, matching the stated school total. Direct totals are 354 boys and 246 girls, so 354 − 246 = 108.
Therefore, the required difference is 108 students.