Question

The mean age of a combined group of men and women is $30$ years. If the mean age of men and women are respectively $32$ and $27$, then the percentage of women in the group is

• A. $30$
• B. $40$
• C. $50$
• D. $60$

Answer 1

Answer: (B)

$40$

Let there be '$m$' men and '$w$' women

According to question, their combined mean is 30

$\therefore \frac{32m+27w}{m+w}=30$

(here 32 is mean age of all men and 27

is mean age of all women)

$32m+27w=30m+30w$

$\Rightarrow 2m=3w\Rightarrow m=\frac{3}{2}w$

Percentage of women in group is

$\{\left(\frac{w}{w+m}\right)\times 100\}\%$

$=\{\left(\frac{w}{w+\frac{3}{2}w}\right)\times 100\}\%$

$=\{\frac{2}{5}\times 100\}\%$

$=40\%$

Answer is option $\left(B\right)$.