Question

The sum of reciprocals of Meena’s ages (in years ) 3 years ago and 5 years hence `1/3` Find her present ages. 

Answer 1

Let the present age of Meena be x years
Meena’s age 3 years ago =(x-3)years 

Meena’s age 5 years hence =(x+5) years 

According 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^2+2x-15)=1/3` 

⇒`x^2+2x-15=6x+6` 

⇒`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=0  or  x+3=0` 

⇒`x=7  or  x=-3` 

∴` x=7 `                      (Age cannot be negative)
Hence, the present age of Meena is 7 years.