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Question

The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5 years from now is 13. Find his present age.


Solution

Let the present age of Rehman be x years.
Three years ago, his age was (x3) years.
Five years hence, his age will be (x+5) years.
It is given that the sum of the reciprocals of Rehman's ages 3 years ago and 5 years from now is 13.
1x3+1x+5=13

x+5+x3(x3)(x+5)=13

2x+2(x3)(x+5)=13

3(2x+2)=(x3)(x+5)

6x+6=x2+2x15

x24x21=0

x27x+3x21=0

x(x7)+3(x7)=0

(x7)(x+3)=0

x=7,3
However, age cannot be negative.
Therefore, Rehman's present age is 7 years.

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