Question:
A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is
A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is
Updated On: Jul 30, 2025
- 9.5
- 10
- 4.5
- 6
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The Correct Option is A
Solution and Explanation
Let the average score of the boys in the mid-semester exam be \( x \). Therefore, the average score of the girls in the mid-semester exam is \( x + 5 \). The total score for boys = \( 20x \) and for girls = \( 30(x + 5) = 30x + 150 \). The average of the entire class in the mid-semester exam is \(\frac{20x + 30x + 150}{50} = x + 3\).
In the final exam, the average score of the girls becomes \(x + 5 - 3 = x + 2\). The entire class's average increases by 2, so it is now \(x + 3 + 2 = x + 5\).
Total score in the final exam is \(\frac{50(x + 5)}{1}= 50x + 250\). The new total score for girls is \(30(x + 2) = 30x + 60\).
The total score for boys in the final exam can be calculated by subtracting the girls' score from the total score: \(50x + 250 - (30x + 60) = 20x + 190\). The average score of boys in the final exam is \(\frac{20x + 190}{20} = x + 9.5\).
The increase in the average score of the boys is \(x + 9.5 - x = 9.5\).
Thus, the increase in the average score of the boys is 9.5.
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