Question

The mean age of combined group of man and woman is 35 years If the mean age of man is 36 years and that of woman is 32 years The percentage of man and woman is the group is respectively given by

• A. Men = 75%, women = 25%
• B. Men = 70%, women = 30%
• C. Men = 50%, women = 50%
• D. Men = 25%, women = 75%

Answer 1

The correct option is A Men = 75%, women = 25%

Combined Mean $\overline{X}=\frac{n_1\overline{X_1}+n_2\overline{X_2}}{n_1+n_2}$

Here $\overline{X}=35,\overline{X_1}=36,\overline{X_2}=32$

$n_1+n_2=100$ (Its denote the number of men and women).

Hence $n_2=100-n_1$

$\Rightarrow 35=\frac{36n_1+32(100-n_1)}{100}$

$\Rightarrow 3500=36n_1+3200-32n_1$

$\Rightarrow 4n_1=3500-3200$

$\Rightarrow 4n_1=300$

$\Rightarrow n_1=\frac{300}{4}=75$

$n_2=100-75=25$

Hence the percentage of men and women is 75% and 25%