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

The correct option is A.

Let the average score of boys in the mid-semester exam be $B_1$.
Then, the average score of girls in the mid-semester exam is $G_1=B_1+5$.

The total score of the class in the mid-semester exam is:
$T_1=20B_1+30(B_1+5)=50B_1+150$
Thus, the average score of the entire class in the mid-semester exam is:
$A_1=\frac{50B_1+150}{50}=B_1+3$

In the final exam:
1. The average score of the girls dropped by 3, so the new average score of girls is:
$G_2=G_1-3=(B_1+5)-3=B_1+2$

2. The average score of the entire class increased by 2, so the new average score of the class is:
$A_2=A_1+2=(B_1+3)+2=B_1+5$

Let the average score of boys in the final exam be $B_2$. The total score in the final exam is:
$T_2=20B_2+30G_2=50A_2$
Substitute $G_2=B_1+2$ and $A_2=B_1+5$ into the equation:
$20B_2+30(B_1+2)=50(B_1+5)$
$20B_2+30B_1+60=50B_1+250$

$B_2=B_1+9.5$

Therefore, the increase in the average score of the boys is:
$B_2-B_1=9.5$