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. 9.5
• B. 10
• C. 4.5
• D. 6

Answer 1

Answer: (A)

9.5

Answer 2

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.