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

The correct option is A

9.5

Let the average score of boys and girls be ‘b’ & ‘g’ respectively.
Given,
$50\times [\left\{\frac{(30g+20b)}{50}\right\}+2]=30\times (g-3)+20\times b_n$, where $b_n$ is the new average score of boys.
$30g+20b+100=30g-90+20b_n{b}_n=b+\frac{19}{2}(b_n–b)=9.5$