The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

Question: The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

Solution:
Average weight of women = 55 kg
Average weight of men = 70 kg
Average weight of the entire group = 65 kg

Let,
the number of men = M.
and, the number of women = W.
Then, the total number of people in the group is (M + W)

ATQ,
55W + 70M = 65(M + W)
Or, 55W + 70M = 65M + 65W
Or, 70M - 65M = 65W - 55W
Or, 5M = 10W
Or, W : M = 1 : 2

∴ The ratio of women to men in the group is 1 : 2.