Question

The mean age of a combined group of men and women is $25\text{yr}$. If the mean age of the group of the men is $26$ and that of the group of women is $21$, then the percentage of men and women in the group is

• A. $46,60$
• B. $80,20$
• C. $20,80$
• D. $60,40$

Answer 1

The correct option is B

$80,20$

Explanation for the correct option.

Compute the percentage of men and women in the group.

Assume that, there are $100$ in the group out of which $x$ are men.

So, there are $100-x$ women in the group.

Since, it is given that the mean age of the men is $26$.

Therefore, the sum of the men's age is $26x$.

Since, it is given that the mean age of the women is $21$.

Therefore, the sum of the women's age is $21(100-x)$.

Since, it is given that the combined mean age is $25\text{yr}$.

Therefore,

$$\begin{gathered} \frac{26x+21(100-x)}{100}=25 \\ \Rightarrow 26x+2100-21x=2500 \\ \Rightarrow 5x=400 \\ \Rightarrow x=80 \end{gathered}$$

Therefore, there are $80$ percent of men in the group and $20$ percent women.

Hence, option $B$ is the correct option.