In Mathopolis, an adult is a person 21 years of age or older and a child is a person under 21 years of age.  Exactly half of the  adults in Mathopolis are female, and exactly half of the female  adults have exactly one biological child.  Nobody else has a  child, and there are no other children.  What percent of the  people of Mathopolis are children?
Let the percentage of people in Mathopolis who are children be $x$. The percentage of adults is then $1-x$. Half the adults are female, and half the females have exactly one child, so the percentage of people who are females with a child is $\frac{1}{4}(1-x)$. This percentage is equal to the percentage of children, since there is a correspondence between a mother and a child. So we have the equation $x=\frac{1}{4}(1-x)$. Solving for $x$ yields $x=1/5$, or $\boxed{20}$ percent.