The sum of the ages of a father and his son is 45 years. Five years ago,the product of their ages (in years) was 124. Determine their presentages.

Let the present age of the father be x years.
Then the present age of the son is (45 – x) years.
Five years ago father's age = x – 5 years
Five years ago son's age = (45 – x) – 5 years = (40 – x) years
Condition: The product of their ages was 124.
(x - 5)(40 - x) = 124
x(40 - x) - 5(40 - x) = 124
40x – x ² - 200 + 5x = 124
- x ² - 324 + 45x = 0
x ² - 45x + 324 = 0
x ² - 36x – 9x + 324 = 0
x(x – 36) – 9(x – 36) = 0
(x – 9)(x – 36) = 0
x – 9 = 0 or x – 36 = 0
x = 9 or x = 36
Fathers age is 36 years and sons age is 9 years.
Checking:
a) 36 + 9 = 45.
b) 31 × 4 = 124.