Question

The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is $\frac{1}{3}$. Find his present age.

Answer 1

SOLUTION :  

Let the present age of Rehman be x years

Rehman’s age 3 years ago = (x – 3) years

5 years later Rehman’s age will be  (x + 5) years

A.T.Q

1/(x – 3 ) + 1/(x + 5) = 1/3  

(x + 5 + x – 3)/(x – 3)(x + 5) = 1/3  

[ By taking LCM]

(2x + 2)/(x2 – 3x + 5x – 15) = 1/3  

(2x + 2)/(x2 + 2x – 15) = 1/3  

x2 + 2x – 15 = 3(2x + 2)

x2 + 2x – 15 = 6x + 6  

x² + 2x - 6x - 15 - 6 = 0

x2 – 4x – 21 = 0  

x² - 7x + 3x - 21 = 0

[By middle term splitting]

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

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

x + 3 = 0 or  x -  7 = 0

x = - 3 or x  = 7  

But, x = - 3 is not possible because age can't be negative. Therefore,  x = 7  

Hence ,Rehman’s present age is 7 years.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

sum of the reciprocal age 3year ago and 5 years from now =1/3

let the present age be =x

=>age of rehman 3year ago is x-3

=>reciprocal=1/x-3

now age of rehman 5year from now be x+5

=>reciprocal= 1/x+t

we have given that 1/x-3+1/x+5=1/3

=>x+5+x-3/(x-3)(x+5)=1/3