# Ex.4.4 Q4 Quadratic Equations Solutions - NCERT Maths Class 10

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## Question

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends are $$20$$ years. Four years ago, the product of their age in year was $$48$$ years.

Video Solution
Ex 4.4 | Question 4

## Text Solution

What is Known?

i) The sum of the ages of two friends are $$20$$ years.

ii) Four years ago, the product of their age in year was $$48$$ years.

What is UnKnown?

Checking the possibility of the situation and if yes, find the present ages.

Reasoning:

Let the age of friend $$1$$ be $$x$$ years.

Then,

i) Age of friend $$2 = 20 \,–$$ age of friend $$1= 20 - x$$

ii) Four years ago, age of friend $$1 = x – 4$$

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

Product of their ages: $$(x - 4)(20 - x - {\rm{ }}4) = 48$$

Steps:

\begin{align}(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\end{align}

Let’s find the discriminant: $$b² - 4ac$$

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

\begin{align}b^2- 4ac& = ( - 20)^2 - 4(1)(112)\\ & = 400 - 448\\& = - 48\\b^2 - 4{ac} &< 0\end{align}

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

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