Answer :

Let age of one friend be x and another friend be (20 – x) so that their sum is 20

Age four years ago

Age of one friend would have been (x – 4) and another friend would have been (20 – x – 4) which is (16 – x)

Given that four years ago the product of their ages was 48

⇒ (x – 4)(16 – x) = 48

⇒ 16x – x^{2} – 64 + 4x = 48

⇒ – x^{2} – 64 + 20x = 48

⇒ x^{2} + 64 – 20x + 48 = 0

⇒ x^{2} – 20x + 112 = 0

Comparing equation x^{2} – 20x + 112 = 0 with ax^{2} + bx + c = 0 we get

a = 1, b = – 20 and c = 112

Discriminant (D) = b^{2} – 4ac

⇒ D = (– 20)^{2} – 4(1)(112)

⇒ D = 400 – 448

⇒ D = –48

D<0 which means no real values of x

As no real values of x the equation which we formed using given statements cannot be true

Hence the statements cannot be true

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