Question

The mean age of a combined group of men and women is 30 years. If the means of the 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

Answer 2

The formula for combined mean is $\bar{\mathbf{x}}\mathbf{=}\frac{\mathbf{n}_{\mathbf{1}}{\bar{\mathbf{x}}}_{\mathbf{1}}\mathbf{+}\mathbf{n}_{\mathbf{2}}{\bar{\mathbf{x}}}_{\mathbf{2}}}{\mathbf{n}_{\mathbf{1}}\mathbf{+}\mathbf{n}_{\mathbf{2}}}$

Given, $\bar{x} = 30$, ${\bar{x}}_{1} = 32$, $\overline{x_{2}} = 27$

Let $n_{1} + n_{2} = 100$ and $n_{1}$ denotes men,$n_{2}$ denotes women for this $n_{2} = 100 - n_{1}$

$30 = \frac{32n_{1} + (100 - n_{1})27}{100}$⇒ $30 = \frac{32n_{1} + 2700 - 27n_{1}}{100}$

⇒ $3000 - 2700 = 32n_{1} - 27n_{1}$⇒$300 = 5n_{1}$⇒$n_{1} = 60$

So, $n_{2} = 40$

Hence, the percentage of women in the group is 40.