Two containers, each of volume $V_0$  , joined by a small pipe initially contain the same gas at pressure  $P_0$ and at absolute temperature $T_0$  . One container is now maintained at the same temperature while the other is heated to  $2T_0$ . If the number of moles of gas in the container at temperature  $2T_0$  is $\frac{n{P}_0{\text{\hspace{0.17em}V}}_0}{3R{T}_0}$  then ‘n’ is

It is not mentioned that the valve connecting the two tubes is opened (or) closed initially/finally. Assumed both in the initial & final states the valves remain closed.
$\Rightarrow V_1^1=V_2^1=V_0$  &  $P_1^1=P_2^1=P^1\mathrm{....}\left(1\right)$
Consider total number of moles is always same 
$n_1+n_2=n_1^1+n_2^1=$  constant ….. (2)
 $=\frac{P_1{V}_1}{T_1}+\frac{P_2{V}_2}{T_2}=\frac{P^1{V}_1^1}{T^{{ }_1^1}}+\frac{P^1{V}_2^1}{T_2^1}$
 $\Rightarrow \frac{2P_0{V}_0}{T_0}=P^1{V}_0\{\frac{1}{T_0}+\frac{1}{2T_0}\}\mathrm{.......}\left(3\right)$

From ideal gas equation (for gas in chamber-2)
 $P_2^1{V}_2^1=n_{2}R{T}_2^1\mathrm{.....}\left(4\right)$
 $\Rightarrow P^1\left(V_0\right)=n_{2}R\left(2T_0\right)\Rightarrow n_2=\frac{2P_0{V}_0}{3R{T}_0}\Rightarrow n=2$