Question

The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

Answer 1

3/5

Explanation:

avg in A = 41

avg in B = 38

combined avg of A and B = 36

Let a = number of people in group A.

Let b = number of people in group B.

The total number of people = a + b.

The sum of all ages in group A is 41a.

The sum of all ages in group B is 36b.

The sum of all ages in the combined group A and B is 38(a + b).

41a + 36b = 38(a + b)

41a + 36b = 38a + 38b

3a = 2b

a/b = 2/3

a/b + 1 = 2/3 + 1

a/b + b/b = 2/3 + 3/3

(a + b)/b = 5/3

b/(a + b) = 3/5