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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. Q.4

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What is the best way for solving this question of quadratic equations, It is very important question for class 10th. How i solve by easy way 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.

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

    Three years ago, Rehman’s age was (x – 3) years.

    Five years after, his age will be (x + 5) years.

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

    ∴ 1/x-3 + 1/x-5 = 1/3

    (x+5+x-3)/(x-3)(x+5) = 1/3

    (2x+2)/(x-3)(x+5) = 1/3

    ⇒ 3(2x + 2) = (x-3)(x+5)

    ⇒ 6x + 6 = x2 + 2x – 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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