Question

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

Answer 1

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

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

Answer 2

Answer:

$\large{\underline{\boxed{\sf Rehman's \: age = 7 \: years. }}}$

Step-by-step explanation:

Let the present age of rehman be x years.

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

And, the age of rehman 5 years from now = (x + 5) years.

According to the question ;

Equation formed:

$\boxed{ \bf \dfrac{1}{x - 3} + \dfrac{1}{x + 5} = \dfrac{1}{3} }$

On solving the above equation ;

$\sf \frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3} \\ \\ \implies \sf \frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3} \\ \\ \implies \sf \frac{x + 5 + x - 3}{x {}^{2} + 5x - 3x - 15} = \frac{1}{3} \\ \\ \implies \sf \frac{2x + 2}{x {}^{2} + 2x - 15} = \frac{1}{3} \\ \\ \bf on \: squaring \: both \: sides : \\ \\ \implies \sf x {}^{2} + 2x - 15 = 3(2x + 2) \\ \\ \implies \sf {x}^{2} + 2x - 15 = 6x + 6 \\ \\ \implies \sf {x}^{2} + 2x - 15 - 6x - 6 = 0 \\ \\ \implies \sf {x}^{2} - 4x - 21 = 0$

Here, we got an equation, it can be solved by splitting the middle term. Here we go;

$\implies \sf {x}^{2} - 4x - 21 = 0\\ \\ \implies \sf x {}^{2} - 7x + 3x - 21 = 0 \\ \\ \implies \sf x(x - 7) + 3(x - 7) = 0 \\ \\ \implies \sf (x - 7)( x+ 3) = 0$

By zero product rule ;

⇒ x = 7 or x = - 3

Since, age can not be negative. We can neglect (-3).

Hence, the age of rehman is 7 years.