Question

The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.

Answer 1

Let the present ages of the boy and his brother be x years and (25-x) years. 
According to the question: 

`x(25-x)=126` 

⇒`25x-x^2=126` 

⇒`x^2-(18-7)x+126=0` 

⇒`x^2-18x-7x+126=0` 

⇒`x(x-18)-7(x-18)=0` 

⇒`(x-18)(x-7)=0` 

⇒`x-18=0  or  x-7=0`  

⇒`x=18  or  x=7` 

⇒ `x=18`              ( ∵Present age of the boy cannot be less than his brother)  

If x 18,we have
Present ages of the boy = 18 years
Present age of his brother =(25-18)years=7 years 

Thus, the present ages of the boy and his brother are 18 years and 7 years, respectively.