Compare class-wise first-class rates: Class X has 30 students with 24 first-class; Class Y has 35 students with 28 first-class. Which class has a higher percentage of first-class students?
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AClass X has more percentage of students getting first class
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BClass Y has more percentage of students getting first class
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CBoth classes have equal percentage of students getting first class
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DNone of the above
Answer
Correct Answer: Both classes have equal percentage of students getting first class
Explanation
Introduction / Context:Comparing counts across groups of different sizes requires converting to percentages or proportions. Here, we compare first-class rates in two classes of unequal strength.Given Data / Assumptions:
- Class X: 24 first-class out of 30.
- Class Y: 28 first-class out of 35.
Concept / Approach:Compute each percentage as (first-class / total) * 100%. Alternatively, reduce each fraction to simplest terms or compare cross-products.
Step-by-Step Solution:
Class X % = 24/30 * 100% = 0.8 * 100% = 80%.Class Y % = 28/35 * 100% = 0.8 * 100% = 80%.Hence, both classes have equal first-class percentages.Verification / Alternative check:Reduce ratios: 24:30 simplifies to 4:5; 28:35 simplifies to 4:5; equal proportions confirm identical percentages.
Why Other Options Are Wrong:
- Class X more / Class Y more: Both claim a difference that does not exist; both are 80%.
- None of the above: There is a correct specific choice—equality.
Common Pitfalls:Comparing raw counts (24 vs 28) without considering class sizes. Always normalize by the total when comparing groups.
Final Answer:
Both classes have equal percentage of students getting first class