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

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

According to the question:

$x(25-x)=126$

$\Rightarrow 25 x-x^{2}=126$

$\Rightarrow x^{2}-(18+7) x+126=0$

$\Rightarrow x^{2}-18 x-7 x+126=0$

$\Rightarrow x(x-18)-7(x-18)=0$

$\Rightarrow(x-18)(x-7)=0$

$\Rightarrow x-18=0$ or $x-7=0$

$\Rightarrow x=18$ or $x=7$

$\Rightarrow x=18 \quad(\because$ Present age of the boy cannot be less than his brother)

If $x=18$, we have :

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.