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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
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B
80, 20
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C
20, 80
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D
40, 60
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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 men
i.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 $$80,20$$ respectively


Mathematics

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