Correct Answer: 90

Solution : Let the average score of boys as B and the average score of girls as G.
Given that $33 \frac{1}{3} \%$ of the students are boys.
The number of boys = 45 × $\frac{1}{3}$ = 15
The number of girls = 45 – 15 = 30
Also, given that the average score of girls is $66 \frac{2}{3} \%$ more than that of boys.
G = B + $\frac{2}{3}$B = $\frac{5}{3}$B
The average score of all the students is the total score divided by the number of students.
⇒ 78 = $\frac{15B + 30G}{45}$
Substituting G = $\frac{5}{3}$B into the equation,
⇒ $78 = \frac{15B + 30 \times \frac{5}{3}B}{45}$
⇒ $78 = \frac{15B + 50B}{45}$
⇒ $78 = \frac{13B}{9}$
⇒ $B=54$
Substituting B = 54 into the equation,
⇒ G = $\frac{5}{3}$B
⇒ G = $\frac{5}{3}$ × 54
⇒ G = 90
Hence, the correct answer is 90.