The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Question

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.

Answer 1

Given, sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48 

Let the age of one of the friends be ‘a’ 

Age of the other friend = 20 – a 

⇒ (a – 4)(20 –a – 4) = 48 

⇒ (a – 4)(16 – a) = 48 

⇒ a² -20a + 64 + 48 = 0 

⇒ a² – 20a + 112 = 0 D = b² – 4ac 

⇒ D = 400 – 4 × 112 = -48 

Thus, roots are not real as D < 0 

The following situation is not possible