Why do two solutes permitted to diffuse simultaneously across a semi-permeable membrane both end up at equal concentrations on both sides?
If we assume that the solvent is the same on both sides of the membrane (or that the solvent itself can penetrate the membrane) then the final equilibrium will have the same concentration across the membrane.  That only translates to "50% of solute b to occur on side 1 and 50% on side 2" if the volumes are equal.

The rate at which solute A moves from left to right is proportional to the rate at which molecules of solute A on the left side randomly collide with the membrane.  This is proportional to the concentration of A in the left side solution.  The presence of molecules for solute B does not affect this process.

The reverse process is also happening with molecules diffusing from right to left at a rate proportional to their concentration in the right side solution. As the concentration on the right side increases to be equal to the concentration on the left, so the diffusion rates become equal and there is zero nett diffusion and the system approaches equilibrium. 

Note that this assumes a "perfect" system where there is no chemical reaction occurring between the solutes or between the solutes and the membrane.  In practice this means that either the interaction between solutes A and B is the same as the interaction between the solutes and the solvent or that the solute molecules are so greatly outnumbered by the solvent molecules that the solute-solute interactions are not significant.

The rate of diffusion of solute A may be different from B (i.e. the proportionality constant between rate and concentration may be different).   This means that before reaching equilibrium the relative concentrations of A and B may change but at equilibrium, the relative concentration will be the same as initially.

If we define "reaching equilibrium" as having some fraction (say 99.99%) of the final concentration then increasing the initial global concentration will increase the lag for both solutes equally and will not change their relative concentrations.