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.
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