In adult Population or a city, 40% men and 30% women are married. What...
L
et men population be = 100.
So the number of married men is = 40.
Definitely, the number of married women will also be 40.
30 women are married in 100. So 40 are married in 100 x 40/30 = 400/3 women population.
Now total population = 100 + 400/3 = 700/3.
Total married population = 40 + 40 = 80.
%age of married population = 80*3*100/700 = 34 2/7%.
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In adult Population or a city, 40% men and 30% women are married. What...
Given:
- 40% of men are married
- 30% of women are married
- No man marries more than one woman and no woman marries more than one man
- No widows and widowers
To find: The percentage of married adult population
Solution:
Let X be the adult population.
Let M be the number of men and W be the number of women.
From the given data, we can write:
- M = 0.4X (40% of X)
- W = 0.3X (30% of X)
Since no man marries more than one woman and no woman marries more than one man, the number of married couples (C) will be equal to the minimum of M and W. In other words, if there are more men than women, some men will remain unmarried, and if there are more women than men, some women will remain unmarried.
Let's consider two cases:
Case 1: M ≤ W
In this case, the maximum number of married couples will be M, i.e., M men will marry M women. The remaining women (W - M) will remain unmarried. Therefore, the total number of married individuals will be 2M, and the percentage of married individuals will be:
2M/X * 100 = 2(0.4X)/X * 100 = 80%
Case 2: M > W
In this case, the maximum number of married couples will be W, i.e., W women will marry W men. The remaining men (M - W) will remain unmarried. Therefore, the total number of married individuals will be 2W, and the percentage of married individuals will be:
2W/X * 100 = 2(0.3X)/X * 100 = 60%
To get the overall percentage of married individuals, we need to consider both cases. Since M = 0.4X and W = 0.3X, we can write:
- If M ≤ W, then W - M ≥ 0, and the percentage of married individuals is 80%.
- If M > W, then M - W < 0,="" and="" the="" percentage="" of="" married="" individuals="" is="" />
Therefore, the overall percentage of married individuals will be a weighted average of these two cases, where the weights are the probabilities of each case:
P(M ≤ W) = P(0.4X ≤ 0.3X) = P(X ≤ 0) = 0 (impossible)
P(M > W) = P(0.4X > 0.3X) = P(X > 0) = 1
Therefore, the overall percentage of married individuals will be:
0.6 * 1 + 0.8 * 0 = 0.6
So, the percentage of married adult population is 60%, which is equivalent to 34 2/7% (rounded to the nearest integer). Therefore, the correct answer is option C.