In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult…
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
$33\dfrac{1}{7}\%$
34%
$34\dfrac{2}{7}\%$
35%
Solution
Let number of men be $M$ and women be $W$. Married men $= 0.4M$, married women $= 0.3W$. Since each married man pairs with exactly one married woman, $0.4M = 0.3W$, so $M/W = 3/4$. Take $M = 3, W = 4$ (total adults $= 7$). Married men $= 1.2$, married women $= 1.2$; married persons $= 2.4$. Percentage $= \dfrac{2.4}{7} \times 100 = \dfrac{240}{7} = 34\dfrac{2}{7}\%$.