# 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

**Solution:**

Let the age of friend 1 be x years.

According to the question, age of friend 2 will be 20 - age of friend 1 = 20 - x

Four years ago, age of friend 1 = x - 4

Four years ago, age of friend 2 = 20 - x - 4

Product of their ages: (x - 4)(20 - x - 4) = 48

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

16x - x^{2} - 64 + 4x = 48

- x^{2} + 20x - 64 = 48

-x^{2} + 20x - 64 - 48 = 0

- x^{2} + 20x - 112 = 0

x^{2} - 20x + 112 = 0

Let’s find the discriminant: b^{2} - 4ac

a = 1, b = -20, c = 112

b^{2} - 4ac = (-20)^{2} - 4(1)(112)

= 400 - 448

= - 48

b^{2} - 4ac < 0

Therefore, there are no real roots. So, this situation is not possible.

**Video Solution:**

## 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

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.4 Question 4:

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

The present ages of two friends can not be calculated for the situation given as the sum of the ages of two friends is 20 years. Four years ago, the product of their age in years was 48 years