the mean age of combined group of men and women is 30 years. if the mean of the age of men and women are respectively 32 and 27, then the percentage of women in the group is ??

Let the number of men and women in the group be m and n respectively.
Hence,
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%