Question

the mean age of a combined group of men and women is 30 years. if the mean age of the men’s group is 32 years and that for the womens group is 27 years, find the percentage of men and women in the combined group

Answer 1

Answer:

Let total no. of people in the group be 100 and out of them x are men

i.e no of women = 100−x.

Mean age =

no of people

sum of ages in the group

Total sum = sum of ages of men + sum of ages of women

⇒100×25=x×26+(100−x)×21

⇒x=80

Hence, the percentage of men and women in the group is 80,20 respectively

Answer 2

Answer:

QUESTION

the mean age of a combined group of men and women is 30 years. if the mean age of the men’s group is 32 years and that for the womens group is 27 years, find the percentage of men and women in the combined group?

ANSWER

sum of the ages of the men in the group = mean age of men × number of men = 32m; and

sum of the ages of the women in the group = mean age of women × number of men = 27n.

Also,

(Sum of ages of men+ Sum of ages of women) /Total people in group = Mean age of group

or (32m + 27n)/(m + n) = 30

or 32m + 27n = 30m + 30n

or 2m = 3n

or m = 1.5n

Percentage of women in the group = 100n/(m+n) = 100n/2.5n = 40%