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

Updated On: Sep 26, 2024
  • 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 examination be b.
The average score of the girls is b+5. 
In the final exam, the average score of the girls is b+5−3=b+2. 
The average score of the entire class increased by 2 and is, therefore, b+2.
\(⇒\frac{20b+30(b+5)}{50}+2\ i.e\ b+5\)
Average score of the boys
\(\frac{50(b+5)-30(b+2)}{20}=b+9.5\)
The increase in the average score of boys is 9.5.

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