$\begin {array} {1 1} (A)\;30 & \quad (B)\;40 \\ (C)\;50 & \quad (D)\;60 \end {array}$

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Let there be $x$ women out of 100 persons.

$\Rightarrow$ No. of men $=100-x$

Given that Mean of combined age of men and women =30

$ \therefore \large\frac{32(100-x)+27x}{100}$ $=30$

$\Rightarrow\: 32 ( 100-x) + 27x=30 \times 100$

$\Rightarrow\: 3200-32x+27x=3000$

$\Rightarrow\: -5x=3000-3200$

$\Rightarrow\: -5x=-200$

$\Rightarrow\: x = \large\frac{-200}{-5}$

or $ x = 40$

Ans : (B)

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