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 |
If P and Q are the differences between the number of boys and girls in class A and class C, respectively, then the percentage of P with reference to Q is
Answer: C. 100% — ConceptTo find one quantity as a percentage of another, divide the first quantity by the reference quantity and multiply by 100. When a total is split in the…
- A.
80%
- B.
120%
- C.
100%
- D.
90%
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
To find one quantity as a percentage of another, divide the first quantity by the reference quantity and multiply by 100.
When a total is split in the ratio a : b, the difference between the two parts is Total × |a − b|/(a + b).
Application
Class A has 20% of 600 = 120 students.
For class A, the boys-to-girls ratio is 3 : 2, so P = 120 × (3 − 2)/(3 + 2) = 24.
Class C has 16% of 600 = 96 students.
For class C, the boys-to-girls ratio is 5 : 3, so Q = 96 × (5 − 3)/(5 + 3) = 24.
Therefore, the percentage of P with reference to Q is (P/Q) × 100 = (24/24) × 100 = 100%.
Cross-check
Direct splitting gives class A as 72 boys and 48 girls, and class C as 60 boys and 36 girls. Both differences are 24, confirming that P and Q are equal and the result is 100%.