  We explore the possibility that the discrepancy in the observed anomalous
magnetic moment of the muon $\Delta a _\mu$ and the predicted relic abundance
of Dark Matter by Planck data, can be explained in a lepto-philic 2-HDM
augmented by a real SM singlet scalar of mass $\sim$ 10-80 GeV. We constrain
the model from the observed Higgs Decay width at LHC, LEP searches for low mass
exotic scalars and anomalous magnetic moment of an electron $\Delta a_e$. This
constrained light singlet scalar serves as a portal for the fermionic Dark
Matter, which contributes to the required relic density of the universe. A
large region of model parameter space is found to be consistent with the
present observations from the Direct and Indirect DM detection experiments.
