The establishment of stationary solution concentration in a growing or evaporating droplet of an ideal binary solution (binary droplet) placed in a vapor mixture of constituting substances and passive gas is described analytically. Relations defining time dependences of solution concentration in a droplet, the number of molecules of each constituting component, and droplet radius are derived at known parameters of the vapor-gas mixture and the initial composition of a binary droplet. The results of calculations of time dependences of aforementioned values are reported for several variants of the initial composition of a droplet and a vapor mixture.