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.
Heya brainly addictor I want to go offline now because of my phone gonna be dead now.
Answers
Let us say, present age of Rahman is x years.
Three years ago, Rehman’s age was (x – 3) years.
Five years after, his age will be (x + 5) years.
Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 1/3.
∴ 1/x-3 + 1/x-5 = 1/3
(x+5+x-3)/(x-3)(x+5) = 1/3
(2x+2)/(x-3)(x+5) = 1/3
⇒ 3(2x + 2) = (x-3)(x+5)
⇒ 6x + 6 = x^2 + 2x – 15
⇒ x^2 – 4x – 21 = 0
⇒ x^2 – 7x + 3x – 21 = 0
⇒ x(x – 7) + 3(x – 7) = 0
⇒ (x – 7)(x + 3) = 0
⇒ x = 7, -3
As we know, age cannot be negative.
Therefore, Rahman’s present age is 7 years.
Answer:
Let, the age of the rehman = x says
3 years ago rehman's age = x-3
After 5 years rehmans age = x+5
Acc to the given condition
➡️1/x-3 + 1/x+5=1/3
➡️X+5+x-3/(x-3)(x+5)=1/3
➡2x+2=(x-3)(x+5)/3
️➡️6x+6=x^2+5x-3x-15
➡️6x+6=x^2+2x-15
➡️X^2+2x-15-6x-6=0
➡️X^2-4x-21=0
➡️X^2+3x-7x-21=0
➡️X(x+3)-7(x+3)=0
➡️(x-7)(x+3)=0
➡️X=7 (or) x=-3
Age cannot be negative
So x=7
️Therefore,
➡️Present age of the rehman =x=7years
➡️3 years ago rehman's age = x-3=7-3=4years
➡️After 5 years rehmans age = x+5=7+5=>12years