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 |
In the given pair of classes, which two classes have an equal number of boys in them?
Answer: C. D and F — Concept For a class, first multiply the total number of students by its percentage share. If the boys-to-girls ratio is b:g, the number of boys is the class…
- A.
A and D
- B.
C and F
- C.
D and F
- D.
E and F
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
For a class, first multiply the total number of students by its percentage share. If the boys-to-girls ratio is b:g, the number of boys is the class total multiplied by b/(b+g).
Application
Class A has 600 × 20% = 120 students; boys = 120 × 3/5 = 72.
Class B has 600 × 12% = 72 students; boys = 72 × 3/4 = 54.
Class C has 600 × 16% = 96 students; boys = 96 × 5/8 = 60.
Class D has 600 × 15% = 90 students; boys = 90 × 8/15 = 48.
Class E has 600 × 21% = 126 students; boys = 126 × 4/7 = 72.
Class F has 600 × 16% = 96 students; boys = 96 × 1/2 = 48.
Comparing the counts 72, 54, 60, 48, 72, and 48 shows that classes D and F each have 48 boys.
Cross-check
For class D, 48 boys and 42 girls total 90 in the ratio 8:7. For class F, 48 boys and 48 girls total 96 in the ratio 1:1. Both calculations match the table.
Therefore, the required pair is D and F.