4. 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’s say, the age of one friend be x years. Then, the age of the other friend will be (20 – x) years. Four years ago, Age of First friend = (x – 4) years Age of Second friend = (20 – x – 4) = (16 – x) years As per the given question, we can write, (x – 4) (16 – x) = 48 16x – x2 – 64 + 4x = 48 – x2 + 20x – 112 = 0 x2 – 20x + 112 = 0 Comparing the equation with ax2 + bx + c = 0, we get a = 1, b = -20 and c = 112 Discriminant = b2 – 4ac = (-20)2 – 4 × 112 = 400 – 448 = -48 b2 – 4ac < 0 Therefore, there will be no real solution possible for the equations. Hence, condition doesn’t exist.