Question

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

Answer 1

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Answer 2

Let his present age be x years.

3 years ago his age was x-3 years.

5 years from now is age will be x+5 years.

sum of Reciprocal of these will be 1/3

so,

1/(x-3) + 1/(x+5) = 1/3

((x+5) + (x-3))/((x-3)*(x+5)) = 1/3

Cross Multiplication

3x+15+3x-9 = (x-3)*(x+5)

6x + 6 = x^2 + 5x - 3x - 15

x^2 +2x - 15 - 6 - 6x = 0

x^2 - 4x - 21 = 0

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

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

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

x = -3(ignore)

x = 7

Present age of Rehman is 7 years.