 Hello friends welcome to the session. I am Alka today. I am going to help you solve the question That is the sum of the reciprocal of Rehman's ages in years three years ago and five years from now is One-third find his present age. So let's start with the solution So let us first of all assume his present age, which is X Therefore Rehman's age three years ago equal to X minus three years and Rehman's age five years hence equal to X plus five years now according to question Some of the reciprocal of his ages three years ago and five years hence is one upon three which can be written as one upon X minus three plus One upon X plus five equal to one upon three On taking LCM we get X plus five plus X minus three upon X minus three into X plus five equal to one upon three This implies two X plus two Upon X square plus two X minus 15 equal to one upon three this implies Three into on cross multiplication we get three into two X plus two Equal to one into X square plus two X minus 15 This implies six X plus six equal to X square plus two X minus 15 This implies X square plus two X minus six X minus 15 minus six equal to zero or we can say X square minus four X minus 21 Equal to zero therefore the equation is X square minus four X minus 21 Equal to zero now we'll split the middle term on splitting we get X square minus seven X plus three X minus 21 equal to zero this implies taking X common X minus seven Plus three common X minus seven equal to zero this implies X minus seven and X plus three equal to zero this implies that X equal to seven and X equal to minus three Now since H cannot be negative therefore X equal to Seven Hence Rehman's present ages seven years. Hope you understood the solution and enjoyed it. Goodbye and take care