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 – x² = 126 

⇒ x² – (18 – 7)x + 126 = 0 

⇒ x² – 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.