Let $x_{1 }, x_2$ be the roots of the equation $x^2-3x+p=0$ and let  $x_3, x_4$ be the roots of the equation $x^2-12x+q=0$ .If the number $x_1 ,x_2 ,x_{3 },x_4$ (in order) form an increasing G.P., then 

It is given that  

$x_{1 }, x_2$ are roots of $x^2-3x+p=0$

$\Rightarrow x_1+x_2=3 , x_1{x}_2=p$

$x_3, x_4$ are roots of $x^2-12x+q=0$ 

$\Rightarrow x_3+x_4=12$ and $x_3{x}_4=q$

It is given that $x_{1 }, x_2 , x_{3 },x_4$ form an increasing G.P. Therefore, 

$x_1=a,x_2=ar,x_3=a{r}^2,x_4=a{r}^3,$ where $r>1$

Now , 

$\left.\begin{array}{ccccc}{x}_1+x_2& =3& \Rightarrow & a(1+r)& =3\\ x_3+x_4& =12& \Rightarrow & a{r}^2(1+r)& =12\end{array}\right\}\Rightarrow r=2$ and $a=1$

$\therefore x_1=1,x_2=2,x_3=4,x_4=8$

Thus , $p=x_1{x}_2=2$ and $q=x_3{x}_4=32\text{.}$