Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Let age of first friend be x years, so age of other friend is (20 - x) years.

Four years ago,

Age of first friend = (x - 4) years and age of second friend = (20 - x - 4) = (16 - x) years.

Given,

Product of their ages in years was 48.

⇒ (x - 4)(16 - x) = 48

⇒ 16x - x² - 64 + 4x = 48

⇒ 20x - x² - 64 = 48

⇒ x² - 20x + 64 + 48 = 0

⇒ x² - 20x + 112 = 0

Comparing x² - 20x + 112 = 0 with ax² + bx + c = 0, we get :

a = 1, b = -20 and c = 112.

Substituting value in b² - 4ac, we get :

⇒ (-20)² - 4 × 1 × 112

⇒ 400 - 448

⇒ -48.

Since, b² - 4ac < 0.

∴ Roots are imaginary.

Hence, the above situation is not possible.