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Home » The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age
CBSE | Class 10 | Exercise 4.3 | Quadratic Equations
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age

Solution:

Let us say, present age of Rehman is x years.

Three years ago, Rehman’s age was \left( x-3 \right) years.

Five years after, his age will be \left( x~+\text{ }5 \right) years.

Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 1/3.

\therefore 1/(x-3~)+\text{ }1/(x-5)\text{ }=\text{ }1/3

(x+5+x-3)/\left( x-3 \right)\left( x+5 \right)\text{ }=\text{ }1/3

\left( 2x+2 \right)/\left( x-3 \right)\left( x+5 \right)\text{ }=\text{ }1/3

\Rightarrow 3\left( 2x~+~2 \right)\text{ }=\text{ }\left( x-3 \right)\left( x+5 \right)

\Rightarrow 6x~+\text{ }6\text{ }=~{{x}^{2}}~+\text{ }2x~\text{ }15

⇒ x2 – 4x – 21 = 0

⇒ x2 – 7x + 3x – 21 = 0

⇒ x(x – 7) + 3(x – 7) = 0

⇒ (x – 7)(x + 3) = 0

⇒ x = 7, -3

As we know, age cannot be negative.

Therefore, Rehman’s present age is 7 years.

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