General consistent equations for the contact values of the pair correlation functions of mixture of hard spheres are obtained using a recently proposed exact equation relating the mixture pair correlation integrals. Specific expressions are obtained when the general equations are combined with pure hard-sphere equations of state. The mixture equations reduce to the appropriate pure values for all the limiting values of the composition and the collision diameters. Consistent mixture equations are derived based on the Carnahan-Starling and the Kolafa pure equations of state. The resulting equations agree well with the exact mixture fourth virial coefficient and the compressibility factor simulation data.