$\therefore u+v=90$                                                                        ...(i)

 $m=\frac{\upsilon }{u}\Rightarrow 2=\frac{\upsilon }{u}\Rightarrow v=2u$                                                  ...(ii)

Putting the value of v in (i), we get

 $u+2u=90\Rightarrow u=\frac{90}{30}=30$

 $\therefore v=2\times 30=60$

Using lens formula, we get

 $\begin{array}{l}\frac{1}{f}=\frac{1}{\upsilon }-\frac{1}{u}\\ \Rightarrow \frac{1}{f}=\frac{1}{60}-\frac{1}{-30}\\ \Rightarrow \frac{1}{f}=\frac{1}{60}+\frac{1}{30}\\ \Rightarrow \frac{1}{f}=\frac{1+2}{60}=\frac{3}{60}\\ \Rightarrow f=\frac{60}{3}\therefore f=20\text{ cm}\text{.}\end{array}$