The sum of the ages of a man and his son is 45 years. Five years ago, the product of their age was 34. What is the age of the son?

Question: The sum of the ages of a man and his son is 45 years. Five years ago, the product of their age was 34. What is the age of the son?

Solution:
Let, the son's age be = x years
So, the man's age is = (45 - x) years

ATQ,
(x - 5) (45 - x - 5) = 34
⇒ (x - 5) (40 - x) = 34
⇒ 40x - x² - 200 + 5x - 34 = 0
⇒ 45x - x² - 234 = 0
⇒ x² - 45x + 234 = 0
⇒ x² - 39x - 6x + 234 = 0
⇒ (x -39) (x - 6) = 0

So, x = 6, or 39
Son's age must be less than father's age.

∴ x = 6