In a class, there are 54 students. $33\frac{1}{3}$% of the number of students are boys and rest are girls. The average score in mathematics of boys is 50% more than that of the girls. If the average score of all the students is 70, then what is the average score of the boys?

90

33\(\frac{1}{3}\) % = \(\frac{1}{3}\)

Number of boys = 54 x \(\frac{1}{3}\) = 18

Number of girls = 54 - 18 = 36

Average score of girls = 2x

Average score of boys = 2x × \(\frac{3}{2}\) = 3x

18 x 3x + 36 x 2x = 54 x 70

54x + 72x = 3780

126x = 3780

x = 30

Average score of boys = 30 x 3 = 90