Three concentric, spherical conducting shells are arranged in vacuum as shown in figure. The electric capacity of the arrangement between ‘A’ and ‘B’ will be ____times of ${\mathrm{\pi \epsilon }}_0\mathrm{A}$

C of inner and middle shell = $C_1=\frac{4\pi {\epsilon }_{0}a\times 2a}{2a-a}=8\pi {\epsilon }_{0}a$ 
C of middle and outer shell = $C_2=\frac{4\pi {\epsilon }_0\left(2a\right)\left(3a\right)}{3a-2a}=24\pi {\epsilon }_{0}a$
Capacity of outer shell =$=C_3=4\pi {\epsilon }_0\left(3a\right)=12\pi {\epsilon }_{0}a$.

Outer surface of outer shell will also have some charge because it is not earthed. Hence its capacity is also to be considered.

${\mathrm{C}}_{\mathrm{eq}}=\frac{{\mathrm{C}}_1({\mathrm{C}}_2+{\mathrm{C}}_3)}{{\mathrm{C}}_1+{\mathrm{C}}_2+{\mathrm{C}}_3}$
 $C_{eq}=\frac{C_1\left(C_2+C_3\right)}{C_1+C_2+C_3}=\frac{8\pi {\epsilon }_{0}a\left(24\pi {\epsilon }_{0}a+12\pi {\epsilon }_{0}a\right)}{8\pi {\epsilon }_{0}a+24\pi {\epsilon }_{0}a+12\pi {\epsilon }_{0}a}=\frac{36\times 8}{44}\pi {\epsilon }_{0}a$

$C_{eq}=\frac{72}{11}\pi {\epsilon }_{0}a$