Answer
The pressure after the stopcock between the two flasks is opened will be the same for both flasks. For the 1st system, the number of gas molecules in the flask with volume 2X will be double of the flask with volume X as the temperature is constant. For the second system, the number of molecules will be equal as the volume is equal.
Work Step by Step
For 1st system:
If $P_1$ is the initial pressure and $P_2$ is final pressure then
$P_1 (2X)=nRT….1$ and $P_2 (3X)=nRT….2$
Compare equation 1 and 2
So $P_1/P_2 =3/2$ or $P_2=2P_1/3$
For 2nd system:
If $P_1$ is the initial pressure and $P_2$ is final pressure then
$P_1 (X)=nRT….1$ and $P_2 (2X)=nRT….2$
Compare equation 1 and 2
So $P_1/P_2 =2/1$ or $P_2=1P_1/2$
