Three concentric conducting spherical shells have radii r, 2r and 3r and charges $q_1,q_{2}and{q}_3$ respectively. Innermost and outermost shells are earthed as shown in figure. The ratio of charges $q_3:q_1$ is  $n:2$. The value of n is
 

Potential of innermost shell is zero
$\therefore \frac{q_1}{r}+\frac{q_2}{2r}+\frac{q_3}{3r}=0$ 
or  $6q_1+3q_2+2q_3=\mathrm{0....}\left(1\right)$
Similarly potential on outmost shell is also zero.
 $\therefore \frac{q_1}{3r}+\frac{q_2}{3r}+\frac{q_3}{3r}=0$
or  $q_1+q_3=-q_2\mathrm{......}\left(2\right)$
Solving equation(1) and (2) we get
 $q_1=-\frac{q_2}{4},\frac{q_3}{q_1}=3$
and  $\frac{q_3}{q_2}=-\frac{3}{4}$