opening valve separating two volatile solutions
There is not enough information to decide, and the question is not clearly worded.
As to the wording, &quot;two volatile solutions (ideal) of pure liquids P and Q respectively,&quot; implies there is no vapor present, yet &quot;vapours can travel through&quot;. What is the volume of each volatile liquid, and the total volume of the containers, including the connecting tubes? If the whole apparatus has no place for vapor, then the pressure is determined by uncompressible liquids.
As to insufficient information, do the two chemicals react? For example, if the liquids are $\ce{HCl(aq)}$ and $\ce{NH3(aq)}$, the resulting $\ce{NH4Cl(aq)}$ would have a far lower vapor pressure than either of the initial reactants.