The fraction of men in a population who are married is 2/3. The fraction of women in the population who are married is 3/5. What fraction of the population is single?

Answer 1

the population has m men and w women.
Assuming that each married person has a single spouse,

2/3 m = 3/5 w
So, m = 9/10 w
So, assume there are 9 men and 10 women.
The given fractions don't give integer results, so we need to multiply the proposed population.

LCM(3,5) = 15, so let's say there are

135 men and 150 women.

2/3 of 135 = 70
3/5 of 150 = 90
So, there are 160 married people out of 285 total.

The single population is 125/285 = 43.9%

Answer 2

sorry - 2/3 of 135 = 90, as expected.
single is 105/285 = 36.8%