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

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Solution

The correct option is B 40
The formula for combined mean is
$¯ ¯ ¯ x = \frac{n_{1} {¯ ¯ ¯ x}_{1} + n_{2} {¯ ¯ ¯ x}_{2}}{n_{1} + n_{2}}$
$G i v e n, ¯ ¯ ¯ x = 30, {¯ ¯ ¯ x}_{1} = 27$
$L e t n_{1} + n_{2} = 100 a n d n_{1} d o n a t e s m e n, n_{2} d e n o t e s w o m e n f o r t h i s n_{2} = 100 - n_{1}$
$30 = \frac{32 n_{1} + (100 - n_{1}) 27}{100} \Rightarrow 30 = \frac{32 n_{1} + 2700 - 27 n_{1}}{100}$
$\Rightarrow 300 - 2700 = 32 n_{1} - 27 n_{1} \Rightarrow 300 = 5 n_{1} \Rightarrow n_{1} = 60$
$S o, n_{2} = 40$
Hence, the percentage of women in the group is 40.

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