Q4.    The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is \frac{1}{3} . Find his present age.

Answers (1)
D Divya Prakash Singh

Let the present age of Rehman be 'x' years.

Then, 3 years ago, his age was (x-3) years.

and 5 years later, his age will be (x+5) years.

Then according to the question we have,

\frac{1}{(x-3)}+\frac{1}{(x+5)} = \frac{1}{3}

SImplifying it to get the quadratic equation:

\Rightarrow \frac{x+5+x-3}{(x-3)(x+5)} = \frac{1}{3}

\Rightarrow \frac{2x+2}{(x-3)(x+5)} = \frac{1}{3}

\Rightarrow 3(2x+2)= (x-3)(x+5)

\Rightarrow 6x+6 = x^2+2x-15

\Rightarrow x^2-4x-21 = 0

\Rightarrow x^2-7x+3x-21 = 0

\Rightarrow x(x-7)+3(x-7) = 0

\Rightarrow (x-7)(x+3) = 0

Hence the roots are: \Rightarrow x = 7,\ -3

However, age cannot be negative

Therefore, Rehman is 7 years old in present.