PRIZE PUZZLE FOR MARCH 2009
In a given population 40% of the men are married and 60% of the women are married. What percentage of the population is married?
The answer is 48% derived as follows:
If the m is the number of men and w the number of women in the population, then 0.4m is the number of men married and 0.6w is the number of women married. We have to assume these two numbers are the same as they are married to one another so 0.4m = 0.6w If x is the answer as a ratio, the question asks for x = (0.4m+0.6w)/(m+w) which is the proportion of persons, men(0.4m) and women(0.6w), in the population of m+w. Substituting 0.4m/0.6 or 2m/3 for w we get x = (0.4m+0.4m)/(m+2m/3) cancelling the m's: x = 0.8/(1 + 2/3) which makes x = 0.48 or 48%