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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.

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.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Dear Student

Let
present age of Rahman 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 = x^2 + 2x - 15
⇒ x^2 - 4x - 21 = 0
⇒ x^2 - 7x + 3x - 21 = 0
⇒ x(x - 7) + 3(x - 7) = 0
⇒ (x - 7)(x + 3) = 0
⇒ x = 7, -3
As we know, age can’t negative.
Therefore, Rahman’s present age is 7 years.

Thanks

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