Question

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 ??

Answer 1

Let the number of men =x
Let the number of women =y
Average age of men=32
Average age of women =27
Average age of total is=30
Then x(32)+y(27)=(x+y)30
2x=3y
x/y=3/2then x: y=3:2
Percent of women =(2/5)100=40

Answer 2

Answer:

The percentage of women in the group is 40%

Step-by-step explanation:

Let the number of men be x

Let the number of women be y

Average age of men=32

$Average = \frac{\text{Sum of ages of men}}{\text{No. of men }}$

$32 = \frac{\text{Sum of ages of men}}{x}$

$32x = \text{Sum of ages of men}$

Average age of women =27

$Average = \frac{\text{Sum of ages of women}}{\text{No. of women }}$

$27= \frac{\text{Sum of ages of women}}{y}$

$27y = \text{Sum of ages of women}$

Average age of total is is 30

$Average = \frac{\text{Sum of ages of women and men}}{\text{No. of men and women }}$

$30= \frac{\text{Sum of ages of men and women}}{x+y}$

$30(x+y) = \text{Sum of ages of men and women}$

$32x+27y=30(x+y)$

$2x=3y$

$\frac{x}{y}=\frac{3}{2}$

So, x: y=3:2

Percent of women =$\frac{2}{5} \times 100=40$

Hence the percentage of women in the group is 40%