Question

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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 years and that of women is 21 years, then find out the percentage of men and women in the group.

Answer 1

Ans % of Men=80 and Women=20

If the number of men=m and women=w, Total age of men & women=26m+21w
Given,Combined Mean Age=25= 26m+21w/(m+w)
25m+25w=26m+21w -->4w=m or m/w=4/1
Therefore % of men=80 and women=20

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Answer 2

Answer:

Percentage of men = 80 %

Percentage of women = 20 %

Step-by-step explanation:

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

Let the total age of all men be a and that of all women be b.

As given, mean of ages of men is 26.

a / x = 26

a = 26 x ---- ( 1 )

Next, mean of ages of women is 21

b / y = 21

b = 21 y ---- ( 2 )

Also, total mean of their ages is 25.

( a + b ) / ( x + y ) = 25

a + b = 25 x + 25 y

From ( 1 ) and ( 2 ),

26 x + 21 y = 25 x + 25 y

x = 4y

Thus, total number of people:

x + y = 4 y + y = 5 y

Percentage of men:

( x / 5 y ) × 100

= ( 4 y / 5 y ) × 100

= ( 4 / 5 ) × 100

= 80 %

Percentage of women:

( y / 5 y ) × 100

= ( 1 / 5 ) × 100

= 20 %