Question

the sum of reciprocals of rehman's age 3 years ago and 5 years from now is1/3.find his present age

Answer 1

Solution:-
Let the present age of Rehman be x years.
So, 3 years age his age was = (x - 3) years
The reciprocal = 1/(x - 3)
And, after 5 years the age will be = (x + 5) years
The reciprocal = 1/(x + 5)
So, according to the question 
1/(x - 3) + 1/(x + 5) = 1/3   Taking L. C. M. of (x - 3) and (x + 5)
(x - 5) + (x - 3)/(x² + 2x - 15) = 1/3
 (2x + 2)/(x² + 2x - 15) = 1/3
6x + 6 = x² + 2x - 15
x² + 2x - 6x - 15 - 6 = 0
x² - 4x - 21 = 0
x² - 7x + 3x - 21 = 0
x(x - 7) + 3(x - 7) = 0
(x - 7)(x + 3) = 0
x = 7 and x = -3
x = - 3 is not possible because age cannot be negative.
So, x = 7
Therefore present age of Rehman is 7 years.
Answer.

Answer 2

Answer:

Let us say, 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 = x2 + 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 cannot be negative.

Therefore, Rahman’s present age is 7 years.