Is this relation in case of a mixture of ideal gases valid?
This relation is not valid if the gases are assumed to be ideal. see Amagat's law of partial volumes
Moreover, if the gases are non ideal, the relations between the volumes of the combining gases and the final resultant volume is very complex and the given relation is too simple and includes too less variables to even begin describing the actual non-ideal gas mixing.
It, however unlikely, might represent a certain special case that can only be judged from the context wherein the aforementioned equation was taken from.