The mean age of combined group of men and women is 25 years. If the mean age of group of men is 26 and that of group of women is 21, then percentage of men and women in the group respectively is :
The total number of people in the group is M + W.
The mean age of men is 26, so the sum of ages of men is 26M.
The mean age of women is 21, so the sum of ages of women is 21W.
The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W).
The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women.
26M + 21W = 25(M + W)
26M + 21W = 25M + 25W
Subtract 25M from both sides:
26M – 25M + 21W = 25W
M + 21W = 25W
Subtract 21W from both sides:
M = 25W – 21W
M = 4W
The number of men is 4 times the number of women.
The total number of people is M + W = 4W + W = 5W.
The percentage of men in the group is (Number of men / Total people) * 100
Percentage of men = (4W / 5W) * 100 = (4/5) * 100 = 80%.
The percentage of women in the group is (Number of women / Total people) * 100
Percentage of women = (W / 5W) * 100 = (1/5) * 100 = 20%.
The percentage of men and women in the group respectively is 80% and 20%.
Mean age of Men (M) = 26
Mean age of Women (W) = 21
Mean age of Combined (C) = 25
Absolute difference between M and C = |26 – 25| = 1
Absolute difference between W and C = |21 – 25| = |-4| = 4
The ratio of the number of Women to Men is the ratio of the differences (M-C) : (C-W) = 1 : 4.
So, W : M = 1 : 4, which means M = 4W.
The ratio of Men to Women is M : W = 4 : 1.
Total parts = 4 + 1 = 5.
Percentage of Men = (4/5) * 100 = 80%.
Percentage of Women = (1/5) * 100 = 20%.