The total number of students in section A and B of a class is 120. The number of students in section A is 30 more than that of section B. The average score of the students in B, in a test, is 22.22% less than that of students in A. If the average score of all the students in the class is 69.3, then what is the average score of the students in A?

75.6

Difference of no. of students = 30

Hence, no. of students in A = 75 and B = 45

Ratio of No. of students ⇒ A : B = 5 : 3

22.22% = +\(\frac{2}{9}\)

Ratio of average score ⇒ A : B = 9 : 7

Now,

Accordingly average of (A + B) = \(\frac{(9 × 5) + (7 × 3)}{5 + 3}\) = \(\frac{66}{8}\) = \(\frac{33}{4}\)

ATQ,

\(\frac{33}{4}\)R = 69.3

1R = 69.3 × \(\frac{4}{33}\)

Average score of A = 9R = 9 × 69.3 × \(\frac{4}{33}\) = 75.6