Question

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

A
60, 40
B
80, 20
C
20, 80
D
40, 60

Solution

## The correct option is A $$80,\space 20$$Let total no. of people in the group be $$100$$ and out of them $$x$$ are meni.e no of women = $$100-x$$.Mean age = $$\displaystyle\frac{sum \ of \ ages \ in \ the\ group}{no \ of \ people}$$Total sum = sum of ages of men + sum of ages of women$$\Rightarrow\quad 100\times 25 = x\times 26+\left(100-x\right)\times 21$$$$\Rightarrow x=80$$Hence, the percentage of men and women in the group is $$80,20$$ respectivelyMathematics

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