Capacitance of an isolated conducting sphere of radius ${\mathrm{R}}_1$ becomes n times when it is enclosed by a concentric conducting sphere of radius ${\mathrm{R}}_2$ connected to earth. The ratio of their radii $\left(\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}\right)$ is 
 

Capacitance of an isolated conducting  

sphere of radius ${\mathrm{R}}_1$, ${\mathrm{c}}_1=4{\mathrm{\pi \epsilon }}_{\mathrm{o}}{\mathrm{R}}_1$
Capacitance of spherical shell of  radius ${\mathrm{R}}_1\mathrm{and}{\mathrm{R}}_2$

 ${\mathrm{c}}_2=4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\frac{{\mathrm{R}}_2{\mathrm{R}}_1}{{\mathrm{R}}_2-{\mathrm{R}}_1}$     
 According to given situation,

${\mathrm{c}}_2={\mathrm{nC}}_1$

$\Rightarrow \frac{4\pi {\epsilon }_o{R}_1{R}_2}{R_2-R_1}=n.4\pi {\epsilon }_o{R}_1$

$\Rightarrow \frac{R_2}{R_2-R_1}=n$

$\Rightarrow \frac{R_2-R_1}{R_2}=\frac{1}{n}\Rightarrow 1-\frac{R_1}{R_2}=\frac{1}{n}$

$\Rightarrow 1-\frac{1}{n}=\frac{R_1}{R_2}$

$\Rightarrow \frac{n-1}{n}=\frac{R_1}{R_2}\Rightarrow \frac{R_2}{R_1}=\frac{n}{n-1}.$