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The sum of tue reciprocal of rehman age 3 yrs ago amd 5 yrs from now is 1/3. Find age.

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Question

The SUM of the RECIPROCAL of Rehman's age 3 years ago and 5 years from now is 1/3. Find their present age.

Step-by-step explanation:

LET the present age of Rehman be X years.

So, 3 years ago, Rehman's age=(x-3) years

And 5 years from now, Rehman's age=(x+5) years

Now according to the question, we've

\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}\\ \\ \implies \frac{x+5+x-3}{(x-3)(x+5)}=\frac{1}{3}\\ \\ \implies \frac{2x+2}{(x-3)(x+5)}=\frac{1}{3}\\ \\ \implies 6x+6=(x-3)(x+5)\\ \\ 6x+6=x^2+5x-3x-15 \\ \\ \implies x^2+2x-15-6x-6=0\\ \implies x^2-4x-21=0\\ \implies x^2-7x+3x-21=0\\ \implies x(x-7) +3(x-7)=0\\ \implies (x-7)(x+3)=0\\ \implies x=7\; or\; x=-3\\ But\ since,\ x\neq-3\\ \therefore The\ present\ age\ of\ Rehman\ is\ 7\ years.


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