Question

The mean age of a group of men and women is 25. The mean of the group of men is 26 while that of women is 21, find out the percentage of men and women in the group.

Answer 1

Let n be the number of women

$mean = \frac {w1 + w2..... Wn} {n} \\ \\ 21 = \frac {w1 + w2 +..... + Wn} {n} \\ \\ 21n = w1 + w2 +.... + Wn$

Let m be the number of men

$mean = \frac{ m1 + m2 +...... Mm} {m}\\ \\ 26m = {m1 + m2 +.... Mm}$

Combined mean :-

$Mean = \frac{w1 + w2 +.... Wn + m1 + m2.... Mm} { m + n} \\ \\ 25 = \frac {21n + 26m} {m + n}$

25(m + n) = 21n + 26m

25m + 25n = 21n + 26m

25n - 21n = 26m - 25m

4n = m

$4 = \frac {m} {n}$

80℅ are men

And

20℅ are women.

Answer 2

Let total no. of people in the group be 100 and out of them x are men

i.e no of women = 100−x.

Mean age =  

no of people

sum of ages in the group

​  

 

Total sum = sum of ages of men + sum of ages of women

⇒100×25=x×26+(100−x)×21

⇒x=80

Hence, the percentage of men and women in the group is 80,20 respectively