**Solution:**

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

16*x – x*^{2} – 64 + 4*x* = 48

* – x*^{2} + 20*x – *112 = 0

*x*^{2} – 20*x + *112 = 0

Comparing the equation with *ax*^{2} + *bx *+ *c* = 0, we get;

*a* = *1*, *b* = -2*0* and *c* = 112

Discriminant = *b*^{2} – 4*ac*

*= (-*20*)*^{2} – 4 × 112

= 400 – 448 = -48

*b*^{2} – 4*ac *< 0

Therefore, there will be no real solution possible for the equations. Hence, the condition doesn’t exist.