The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.

Question: The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.

Solution: Average age of children = 12 years
Average age of adults = 32 years
Average age of the entire group = 20 years

Let, the number of adults = A
and, the number of children = C

Then, the total number of people in the group is (C + A)

ATQ,
12C + 32A = 20(C + A)
Or, 12C + 32A = 20C + 20A
Or, 32A - 20A = 20C - 12C
Or, 12A = 8C
Or, C : A = 12 : 8
Or, C : A = 3 : 2

∴ The ratio of children to adults in the group is 3 : 2.