The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.
Answers
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,
=> 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.
Answer:
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{x \: {5} \: + \: x \: - \: {5}}{(x \: - \: {3}) \: (x \: + \: 5)} \: \: = \: \: \frac{1}{3}⇝
(x−3)(x+5)
x5+x−5
=
3
1
=> 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.