Question

The mean age of a combined group of men and women is 30.5 years. If the mean age of the group of men is 35 and that of the group of women is 25, find out the percentage of men and women in the group.

Answer 1

Let the percentage of male in the combined mean be x
∵ percentage of women = (100 − x)

Note: Total of the percentage= 100

Given:

$$\begin{gathered} {\overline{X}}_{m,w}=30.5 \\ {\overline{X}}_m=35 \\ {\overline{X}}_w=25 \end{gathered}$$

We know,
$$\begin{gathered} CombinedMean\left({\overline{X}}_{m,w}\right)=\frac{N_m\times \overline{X_m}+N_w\times \overline{X_w}}{N_m+N_w} \\ or,30.5=\frac{35\times x+25\times (100-x)}{100} \\ or,3050=35x-25x+2500 \\ or,10x=550 \\ or,x=\frac{550}{10} \\ \Rightarrow x=55 \end{gathered}$$

∴ Males = 55%
∴ Women= (100 − x) = (100 − 55) = 45%

Therefore, there are 55% men and 45% women in the group.