The number of students in a class is 45, out of which $$33\frac{1}{3}\% $$  are boys and the rest are girls. The average score of girls is Science is $$66\frac{2}{3}\% $$  more than that of boys. If the average score of all the students is 78, then the average score of girls is:

A. 54

B. 65

C. 78

D. 90

Answer: Option D

Solution(By Examveda Team)

Number of students = 45
Number of boys = $$33\frac{1}{3}\% $$  of 45 = 15
Number of girls = 45 - 15 = 30
Obtain marks of girls in science subject is $$66\frac{2}{3}\% $$  more then the obtain marks of boys.
$$\eqalign{ & 66\frac{2}{3}\% = \frac{2}{3} \cr & \frac{{{\text{Girls}}}}{{{\text{Boys}}}} = \frac{{5x}}{{3x}} \cr} $$
Total marks
15 × 3x + 30 × 5x = 45 × 78
3x + 2 × 5x = 3 × 78
13x = 3 × 78
x = 3 × 6
x = 18
5x = 18 × 5
5x = 90