The average weight of the students in four sections A, B, C and D is 60 kg. The average weight of the students of A, B, C and D individually are 45 kg, 50 kg, 72 kg and 80 kg, respectively. If the average weight of the students of section A and B together is 48 kg and that of B and C together is 60 kg. What is the ratio of the number of the students in sections A and D?

Let number of students in the sections
A, B, C and D be a, b, c and d respectively.
Then, total weight of students of sections A = 45a
Total weight of students of section B = 50b
Total weight of students of section C = 72c
Total weight of students of section D = 80d
According to the question,
Average weight of students of sections of A and B = 48 kg
⇒ (45a + 50b)/(a + b) = 48
⇒ 45a +50b = 48a + 48b
⇒ 3a = 2b
⇒ 15a = 10b
And average weight of students of sections B and C = 60 kg
⇒ 50b + 72c = 60(b + c)
⇒ 10b = 12c
Now, average weight of students of A, B, C and D = 60 kg
∴ 45a + 50b + 72c + 80d = 60(a + b + c + d)
⇒ 15a + 10b - 12c - 20d = 0
⇒ 15a = 20d
⇒ a : d = 4 : 3