Question

The sum of reciprocals of Rehman's age three years and 5 years ago is 1/3. Find his present age.

Answer 1

HEYA!!!

Here is your answer :

Let ,

the present age of Rehman be x years

Before 3 years age of Rehman = ( x -3) years

After 3 years age of Rehman = ( x +5) years

Reciprocal of age of Rehman = 1/3

ATP,

$\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3} \\ \\ \frac{ x + 5 + x - 3}{(x - 3)(x + 5)} \\ \\ \frac{2x + 2}{ {x}^{2} + 5x - 3x - 15} = \frac{1}{3} \\ \\ 6x + 6 - {x}^{2} + 2x - 15 = 0 \\ \\ {x}^{2} - 12x - 6x - 15 - 6 = 0 \\ \\ {x}^{2} - 4x - 21 = 0 \\ \\ after \: splitting \\ \\ {x}^{2} - 7x + 3x - 21 = 0 \\ \\ x(x - 7) + 3(x - 7) = 0 \\ \\ x - 7 = 0 \: \: \: x + 3 = 0 \\ \\ x = 7 \: \: \: \: x = - 3$

The age will not be negative so, the present age of Rehman is 7 years..

HOPE THIS HELPS U.

Answer 2

Hi Rehan ,

Let the age of Rehman be 'x'

So his age before 3 years is ' ( x - 3 ) '

And after 5 years is ' ( x + 5 ) '

Sum of its reciprocals is ⅓

so...

$\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3} \\ \\ \frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3} \\ \\ \frac{2x + 2}{ {x}^{2} + 2x - 15 } = \frac{1}{3} \\ \\ {6x + 6} = {x}^{2} + 2x - 15 \\ \\ {x}^{2} - 4x - 21 = 0 \\ \\ by \: splitting \: the \: middle \: term \\ \\ {x}^{2} + 3x - 7x - 21 = 0 \\ \\ x \times (x + 3) - 7 \times (x + 3) = 0 \\ \\ (x - 7)(x + 3) = 0 \\ \\ x = 7 \: or \: - 3$


Age can't be in negative

So Rehman's age is 7


Hope it helps

Note :- Plz Check the question before you post....