Question

The sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is 1/3. Find the present age.

Answer 1

Let Rehman’s present age be ‘a’. 

Given, sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is 1/3. 

1/(a – 3) + 1/(a + 5) = 1/3 

⇒ 3(a – 3 + a + 5) = a² + 2a – 15 

⇒ a² - 4a – 21 = 0 

⇒ a² – 7a + 3a – 21 = 0 

⇒ a(a – 7) + 3(a – 7) = 0 

⇒ (a + 3)(a – 7) = 0 

⇒ a = 7