Q. 5. The average marks obtained by students of section A of a class is 80 and that of their counterparts from section B was 70. The mean marks obtained by students from both sections A and B was 78. Find the percentage of students from section A. (Dec. 2000)

Solution. Let the mean marks obtained by students of section A = x₁
Let the mean marks obtained by students of section B = x₂
Let the mean marks obtained by students from both sections A and B = x
Here, x₁ = 80, x₂ = 70, x = 78
x = (n₁ X x₁ + n₂ X x₂)/(n₁ + n₂)....... (i)

Putting the values of x, x₁, and x₂ in equation (i), we get
78 = (n₁ X 80 + n₂ X 70)/(n₁ + n₂)
or 8 n₂ = 2 n₁
or n₁/n₂ = 4/1

Therefore, the percentage of students from section A = [4/(4 + 1)] X 100 = 80%.