Let’s say the age of one friend is 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 – $ x^{2} – 64 + 4x$ = 48
– $ x^{2}+ 20x – 112$ = 0
$ x^{2} – 20x + 112$ = 0
Comparing the equation with $ ax^{2} + bx + c$ = 0, we get
a = 1, b = -20 and c = 112
Discriminant = $ b^{2} – 4ac$
= $ (-20)^{2} – 4$ × 112
= 400 – 448 = -48
$ b^{2} – 4ac$ < 0
Therefore, there will be no real solution possible for the equations. Hence, the condition doesn’t exist.