The mean age of a combined group of men and ' women is$25$ years. If the mean age of the group of men is$26$ and that of the group of women is $21$, then the percentage of men in the group is

Let number of men$= n$ and number of women$= m$

$\therefore \sum$ age of $men=n\times 26,\sum$ age of women $=m\times 21$

Combined mean $=\frac{n\times 26+m\times 21}{m+n}=25$

$\Rightarrow 26n+21m=25m+25n\Rightarrow n=4m$

$\%\text{ of men }=\frac{n}{m+n}\times 100=\frac{n}{\frac{1}{4}n+n}\times 100=\frac{4n}{5n}\times 100=80\%$

$\%$ of women $=\frac{m}{m+n}\times 100=\frac{m}{5m}\times 100=20\%$