Q4 of 58 Page 123

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

Let age of one friend be x ,other 20 - x

Four years ago there age was (x - 4) ,(16 - x)


Product of age four years ago = 48


So we can say,


(x - 4)(16 - x) = 48


⇒ x2 - 20x + 112 = 0


Discriminant = (- 20)2 - 4 × 1 × 112 = - 48


Since the discriminant is negative so the roots of the equation are imaginary.


Answer: The above situation is not possible


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