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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.
Solution
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.
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