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

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Q: 116 (CAPF/2009)
The mean age of combined group of men and women is 25 years. If the mean age of group of men is 26 and that of group of women is 21, then percentage of men and women in the group respectively is :

question_subject: 

Maths

question_exam: 

CAPF

stats: 

0,6,5,4,6,1,0

keywords: 

{'mean age': [0, 0, 1, 0], 'percentage': [1, 2, 2, 3], 'men': [4, 3, 12, 9], 'women': [9, 8, 22, 46], 'group': [0, 1, 0, 0], 'years': [1, 0, 0, 2]}

In this question, we are given that the mean age of a combined group of men and women is 25 years. We are also given that the mean age of the group of men is 26 and the mean age of the group of women is 21.

To find the percentage of men and women in the group, we can use the concept of weighted averages.

Let the number of men in the group be x and the number of women be y.

The sum of the ages of the men is x * 26, and the sum of the ages of the women is y * 21.

The mean age of the combined group is given by the equation:

(26x + 21y)/(x + y) = 25

Simplifying this equation, we get:

26x + 21y = 25(x + y)

26x + 21y = 25x + 25y

26x - 25x = 25y - 21y

x = 4y

We know that x + y is the total number of people in the group. So, x + y = (4y) + y = 5y.

Using this information, we can calculate the percentage of men