Question

the sum of the reciprocal of rehmans ages( in years) 3 years ago and 5 years fromnoe is 1/3. Find its present age

Answer 1

Rehman's present age=7years

Answer 2

Given:-

• The sum of the reciprocal of rehmans ages 3 years ago and 5 years from one is 1/3.

To find:-

• Find its present age

Solutions:-

Let the present age of Rehman be x years.

Three years age his age was (x - 3) years.

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

The sum of the reciprocals of Rehman's ages 3 years age and 5 years from now is 1/3.

Therefore,

$\leadsto \: \: \frac{1}{x \: - \: {3}} \: + \: \frac{1}{x \: + {5}} \: \: = \: \: \frac{1}{3}$

$\leadsto \: \: \frac{x \: {5} \: + \: x \: - \: {5}}{(x \: - \: {3}) \: (x \: + \: 5)} \: \: = \: \: \frac{1}{3}$

=> 3(2x + 2) = (x - 3)(x + 5)

=> 6x + 6 = x² + 2x - 15

=> x² - 4x - 21 = 0

=> x² - 7x + 3x - 21 = 0

=> x(x - 7) + 3(x - 7) = 0

=> (x - 7) (x + 3) = 0

=> x = 7, -3

Age cannot be negative.

Therefore, Rehman's present age is 7 years.