The average score in Mathematics of 90 students of sections A and B together is 49. The number of students in A was 25% more than that of B, and the average score of the students in B was 20% higherthan that of the students in A. What is the average score of the students in A?

Let the number of students in section B be x.

The number of students in A was 25% more than that of B. So,

The number of students in A = x $$\times \frac{125}{100}$$ = 1.25x

Total student = 90

x + 1.25x = 90

x = 40

The number of students in B = 40

The number of students in A = 90 - 40 = 50

Let the average score of the section A be p.
Total score of the section A = number of students $$times$$ average = 50p

Average score of the section B = 120% of p = 1.2p

Total score of the section B = 40 $$\times 1.2p = 48p

Total score of 90 students = 49 $$\times 90 = 4410

Total score of the section A + Total score of the section B = 4410

50p + 48p = 4410

p = 4410/98 = 45

$$\therefore$$Average score of the section A is 45.