A time-dependent quantum mechanical approach has been used to investigate the reaction He+HD+(v=0-4,j=0-3)--> HeH++D; HeD++H in three dimensions for total angular momentum J=0. The vib-rotation (v,j) state-selected reaction probability (P-v,j(R)) is shown to increase with v over the collision energy (E-trans) range (0.95-2.25 eV) investigated for both the exchange channels, in accord with the experimental results. The isotopic branching ratio Gamma=P-R(HeH+)/P-R(HeD+) generally remains less than unity for different v states at different E-trans in agreement with experiment. But at E-trans=1.0 eV, for v=4, Gamma obtained from our calculations for j=0 of HD+ is similar to 0.8, in excellent agreement with the earlier quasiclassical trajectory calculations, but a factor of 2 less than that obtained from experiment. This difference could arise from the inclusion of nonzero j states in the experimental study, as P-v,j(R) is found to be j dependent for both the channels. While P-v,j(R) (HeH+) decreases initially with increase in j from 0 to 2 and then increases when j is increased further to 3, P-v,j(R) (HeD+) reveals an unusual j dependence; it is larger for even j states of HD+ than for odd j. As a result, Gamma is strongly dependent on j, in contrast to the marginal dependence shown by the earlier quasiclassical trajectory calculations.