The sum of a father's age and his son's age is 100 years. One-tenth of the product of their ages exceeds the father's age by 180. How old is the son?

Let the son's age be $x$, so the father's age is $100-x$. The condition gives $\frac{1}{10}x(100-x)=(100-x)+180$. Simplifying, $100x-x^2=2800-10x$, so $x^2-110x+2800=0=(x-70)(x-40)$. So $x=70$ or $x=40$. If the son were 70, the father would be 30, which is impossible, so the son is 40 years old.