The sum of the reciprocals of $A$'s ages (in years) 2 years ago and 2 years from now is 2/3. The present age of $A$ is

Explanation

Join (448) ## Page 47 Let A’s present age be x. The sum of the reciprocals of A’s age 2 years ago (x-2) and 2 years from now (x + 2) is given by– $$ \frac{1}{(x - 2)} + \frac{1}{(x + 2)} $$ According to the question– $$ \frac{1}{x - 2} + \frac{1}{x + 2} = \frac{2}{3} $$ $$ \frac{x + 2 + x - 2}{x^2 - 4} = \frac{2}{3} $$ $$ \frac{2x}{x^2 - 4} = \frac{2}{3} $$ $$ 3x = x^2 - 4 $$ $$ x^2 - 3x - 4 = 0 $$ $$ x^2 - 4x + x - 4 = 0 $$ $$ x(x - 4) + 1(x - 4) = 0 $$ $$ x = 4, -1 $$ Hence, the answer is 4 years.