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.
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.

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

According to the question:

\begin{array}{l} x(25-x)=126 \\ \Rightarrow 25 x-x^{2}=126 \\ \Rightarrow x^{2}-(18-7) x+126=0 \\ \Rightarrow x^{2}-18 x-7 x+126=0 \\ \Rightarrow x(x-18)-7(x-18)=0 \\ \Rightarrow(x-18)(x-7)=0 \\ \Rightarrow x-18=0 \text { or } x-7=0 \\ \Rightarrow x=18 \text { or } x=7 \\ \Rightarrow x=18 \quad(\because \text { Present } \\ \text { If } x=18, \text { we have } \end{array}

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.