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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.


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Solution

Step 1: Let us assume, The present age of Rahman is x years.

Three years ago, Rehman’s age was (x3) years.

Five years after, his age will be (x+5) years.

Given that,

The sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 13.

1x-3+1x+5=13(x+5+x-3)(x-3)(x+5)=13(2x+2)(x-3)(x+5)=13

Step 2: Simplify the equation

3(2x+2)=(x-3)(x+5)6x+6=x2+2x15x24x21=0x27x+3x21=0x(x7)+3(x7)=0(x7)(x+3)=0x=7,-3

As we know, age cannot be negative.

Hence, Rahman’s present age is 7 years.


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