# 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 the first friend be x years.

According to the question, age of the second friend will be 20 - age of the first friend = 20 - x

Four years ago, age of the first friend = x - 4

Four years ago, age of the second friend = 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.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 4

**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

**Summary:**

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

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