An exact analysis of the flow of an incompressible viscous fluid past an infinite vertical plate is carried out on taking into account the presence of foreign mass or constant mass flux and ramped wall temperature. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. Two different solutions for the fluid velocity are obtained – one valid for the fluids of Schmidt numbers different from unity, and the other for which the Schmidt number is unity. The effects of different parameters like Prandtl number (Pr), Schmidt number (Sc), time (t) and mass to thermal buoyancy ratio parameter (N) for both aiding and opposing buoyancy effects on the velocity and skin-friction are studied. Also, the heat and mass transfer effects on the flow near a ramped temperature plate has been compared with the flow near a plate with constant temperature.