Estimation of residence time of groundwater, particularly in regions with inadequate surface waters are very important for formulating sustainable groundwater management policies. We developed a technique for extracting dissolved inorganic carbon (DIC) quantitatively from water for measuring its 14C contents and presented the analytical details here. We also measured stable carbon isotope ratio (δ13C) in soil CO2 and groundwater DIC to correct the groundwater 14C ages. In addition, 14C in soil CO2 were measured for making necessary correction in the initial activity of the recharging water. The corrected 14C contents in the groundwater samples were used to estimate their residence times employing Lumped Parameter Models (LPM), a set of mathematical models to account for the processes that take place during transport from the recharge to the sampling spots. We present a case study focused on the calculation of radiocarbon ages and residence times for a groundwater sample collected from the campus of Physical Research Laboratory in Ahmedabad, Gujarat, India. The study also includes estimations of groundwater residence times using previously measured 14C ages of groundwater samples from Gujarat, India. Various factors controlling the groundwater ages in the LPM and their applicability are discussed.