Question:
In a class, 60% of students are boys, and 40% are girls. If 30% of boys and 20% of girls passed an exam, what percentage of the class passed?
In a class, 60% of students are boys, and 40% are girls. If 30% of boys and 20% of girls passed an exam, what percentage of the class passed?
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Assume 100 as the total for percentage problems to simplify calculations, then verify with weighted sums.
Updated On: Jul 29, 2025
- 26%
- 28%
- 30%
- 32%
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The Correct Option is A
Solution and Explanation
We need to find the percentage of the class that passed the exam.
- Step 1: Assume total students. To simplify, assume 100 students (since percentages are given).
- Step 2: Calculate boys and girls. Boys = \( 60% \times 100 = 60 \). Girls = \( 40% \times 100 = 40 \).
- Step 3: Calculate passers.
- Boys passed: \( 30% \times 60 = 0.3 \times 60 = 18 \).
- Girls passed: \( 20% \times 40 = 0.2 \times 40 = 8 \).
- Step 4: Total passers.
\[ 18 + 8 = 26 \] - Step 5: Compute percentage.
\[ \frac{26}{100} \times 100 = 26% \] - Step 6: Alternative approach. Use weighted percentages:
\[ (0.6 \times 0.3) + (0.4 \times 0.2) = 0.18 + 0.08 = 0.26 = 26% \] - Step 7: Check options.
- (a) 26%: Correct.
- (b) 28%: Incorrect.
- (c) 30%: Incorrect.
- (d) 32%: Incorrect.
- Step 8: Verify. Recalculate: Boys’ contribution = \( \frac{18}{100} = 18% \), girls’ = \( \frac{8}{100} = 8% \), total = 26%. Correct.
Thus, the answer is a.
- Step 1: Assume total students. To simplify, assume 100 students (since percentages are given).
- Step 2: Calculate boys and girls. Boys = \( 60% \times 100 = 60 \). Girls = \( 40% \times 100 = 40 \).
- Step 3: Calculate passers.
- Boys passed: \( 30% \times 60 = 0.3 \times 60 = 18 \).
- Girls passed: \( 20% \times 40 = 0.2 \times 40 = 8 \).
- Step 4: Total passers.
\[ 18 + 8 = 26 \] - Step 5: Compute percentage.
\[ \frac{26}{100} \times 100 = 26% \] - Step 6: Alternative approach. Use weighted percentages:
\[ (0.6 \times 0.3) + (0.4 \times 0.2) = 0.18 + 0.08 = 0.26 = 26% \] - Step 7: Check options.
- (a) 26%: Correct.
- (b) 28%: Incorrect.
- (c) 30%: Incorrect.
- (d) 32%: Incorrect.
- Step 8: Verify. Recalculate: Boys’ contribution = \( \frac{18}{100} = 18% \), girls’ = \( \frac{8}{100} = 8% \), total = 26%. Correct.
Thus, the answer is a.
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