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 |
Number of boys in class B is ________% more than the number of girls in class F.
Answer: B. 12.5% — ConceptWhen a whole is divided in a ratio a : b, the first share is a/(a+b) of the whole and the second share is b/(a+b) of the whole. To find how much one…
- A.
8.5%
- B.
12.5%
- C.
15%
- D.
17.5%
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Concept
When a whole is divided in a ratio a : b, the first share is a/(a+b) of the whole and the second share is b/(a+b) of the whole.
To find how much one quantity is more than another, use ((larger - smaller)/smaller) × 100%.
Application
Class B has 12% of 600 students: (12/100) × 600 = 72.
The boys-to-girls ratio in B is 3 : 1, so boys in B = (3/4) × 72 = 54.
Class F has 16% of 600 students: (16/100) × 600 = 96.
The boys-to-girls ratio in F is 1 : 1, so girls in F = (1/2) × 96 = 48.
Percentage more = ((54 - 48)/48) × 100% = (6/48) × 100% = 12.5%.
Cross-check
Increasing 48 by 12.5% gives 48 + (12.5/100) × 48 = 48 + 6 = 54, which matches the independently calculated number of boys in B.
Therefore, the required percentage is 12.5%.