Question

Find the present ages of two friends, if the sum of their ages is 20. Also five years ago, the product of their ages in years was 64.
1. 10, 10
2. 15, 5
3. 12, 8
4. Not possible

Answer 1

Correct Answer - Option 4 : Not possible

Given∶∶

Sum of the ages of two friends = 20

5 years ago, the product of their ages in years was 64.

Formula Used∶

Concept of Quadratic Equations; Discriminant, D = b² – 4ac

If D > 0, then quadratic equation has two unequal real roots.

If D = 0, then quadratic equation has two equal real roots.

If D < 0, then quadratic equation has no real roots.

Calculation∶

Let the present age of one friend be x years

Then the present age of other friend be (20 – x) years

Five years ago, age of one friend was (x – 5)

And the age of another friend was (20 – x – 5) = (15 –x) years

According to the question,

(x -5)(15 – x) = 64

15x – x² – 75 + 5x = 64

x² – 20x + 139 = 0

Now use, Discriminant, D = b² – 4ac

Here, a = 1, b = -20, c = 139

So, D = b² – 4ac = (-20)² – 4 × 1 × 139 = 400 – 556 = - 156

D = - 156

So, D < 0

∵ No real roots exist.

∴ The given situation is not possible.