Addition of co-solvents could introduce perturbation in the H-bond dynamics of water and the extent of perturbation is mostly dependent on the H-bond formation affinity of the respective co-solvent. In this contribution we have studied the H-bond dynamics of water in presence of two co-solvents, 1,2-dimethoxy ethane (DME) and dimethyl sulfoxide (DMSO) using two complementary experimental techniques to compare global (through dielectric relaxation study in the GHz-THz frequency domain) as well as local (through FTIR and optical single color pump-probe studies) hydration environment and dynamics in the two binary mixtures. Due to the presence of sulfur atom DMSO tends to form H-bonds with polar water molecules and subsequently forms various stable H-bonded clusters. DME, owing to its higher carbon content and being a planer molecule, struggles to form H-bonds. DME is rather inclined to form …