# Ex.4.3 Q4 Quadratic Equations Solutions - NCERT Maths Class 10

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## Question

The sum of the reciprocals of Rehman’s age (in years) $$3$$ years ago and $$5$$ years from now is \begin{align}\frac{1}{3} \end{align}. Find his present age.

Video Solution
Ex 4.3 | Question 4

## Text Solution

What is Known?

i) Sum of reciprocals of Rehman’s age (in years) $$3$$ years ago and $$5$$ years from now is \begin{align}\frac{1}{3} \end{align}.

What is Unknown?

Rehman’s age.

Reasoning:

Let the present age of Rehman be $$x$$ years.

$$3$$ years ago, Rehman’s age was $$= x - 3$$

$$5$$ years from now age will be $$= x + 5$$

Using this information and the given condition, we can form the following equation:

\begin{align}\frac{1}{{x - 3}} + \frac{1}{{x + 5}} = \frac{1}{3} \end{align}

Steps:

\begin{align}\frac{1}{{x - 3}} + \frac{1}{{x + 5}} = \frac{1}{3} \end{align}

By cross multiplying we get:

\begin{align}\frac{{(x + 5) + (x - 3)}}{{(x - 3)(x + 5)}} &= \frac{1}{3}\\\frac{{2x + 2}}{{{x^2} + 2x - 15}} &= \frac{1}{3}\2x + 2)(3) &= {x^2} + 2x - 15\\6x + 6 &= {x^2} + 2x - 15\\{x^2} + 2x - 15 &= 6x + 6\\{x^2} + 2x - 15 - 6x - 6 &= 0\\{x^2} - 4x - 21 &= 0\end{align} Finding roots by factorization: \begin{align}{x^2} - 7x + 3x - 21& = 0\\x(x - 7) + 3(x - 7) &= 0\\ (x - 7)(x + 3)& = 0\\x - 7 &= 0 \quad x + 3 = 0\\x &= 7 \quad x = - 3\end{align} Age can’t be a negative value. \(\therefore \; Rehman’s present age is $$7$$ year.

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