Three positive numbers form an increas-ing G.P. If the middle term in this G.P. is tripled, the new numbers are in A.P. Then the common ratio of G.P.is:

Let the three positive numbers in the increas-ing G.P. be

$\frac{a}{r},a,ar$ where $r>1$

We are given, $\frac{a}{r }, 3a, ar$are in A.P. 

$\begin{array}{l}\therefore \hspace{0.25em} \hspace{0.25em}\hspace{0.25em} \hspace{0.25em}\frac{a}{r}+ar=2\left(3a\right)\\ \Rightarrow \hspace{0.25em} \hspace{0.25em} \hspace{0.25em}\hspace{0.25em}{r}^2-6r+1=0\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} r=3\pm 2\sqrt{2}\end{array}$

As           $r>1, r=3+2\sqrt{2}$