(b) Let a, b, c and d be the number of students in class A, B, C and D, respectively.
Then, total marks in section A = 45a
Total marks in section B = 50b
Total marks in section C = 72c
Total marks in section D = 80d
Now, average marks of the students of sections A. B, C andD = 60
∴
= 60
= 45a + 50b + 72c + 80d = 60a + 60b + 60c + 60d
⇒ 15a + 10b -12c - 20d = 0
⇒ 15a +10b =12c + 20d ...........(i)
Also, average marks of the students in sections A and B = 48
= 48
⇒ 45a + 50b = 48a + 48b
⇒ 3a = 2b ................(ii)
and average marks of students in sections B and C = 60
= 60
⇒ 50b + 72c = 60b + 60c
⇒ 12c =10b ...................(iii)
Putting the value of 12c from Eq. (iii) In Eq. (i), we get
15a + 10b = 10b + 20d
⇒ 15a = 20d
⇒ a : d = 20 : 15 = 4 : 3