Q. The mean age of a combined group of men and women is 25 yr. 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 and women in the group is
A) 46, 60
B) 80, 20
C) 20, 80
D) 60, 40
Explanation
(b)
Let $n_{1}and\$ $n_{2}$ be the number of men and women in a group. According to the given condition,
$\frac{n_{1} \times 26 + n_{2} \times 21}{n_{1} + n_{2}} = 25$
$\Rightarrow 26n_{1} + 21n_{2} = 25n_{1} + 25n_{2}$
$\Rightarrow n_{1} = 4n_{2} \Rightarrow \frac{n_{1}}{n_{2}} = \frac{4}{1}$
$\Rightarrow \frac{n_{1}}{{\ n}_{2}} = \frac{80}{20}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.