The close similarity between the Indian census, Government of India and U.N. population estimates and those from the Constrained Coalition and Logistic Model (CCLM) has been demonstrated which enhances the usage of differential equation modeling for studies on population growth processes. The CCLM incorporates the legitimate requirement of an upper bound for the aggregate population thereby implying the rate of natural increase to reach the zero level. The numerical value assumed for the upper bound is based on food supply - arable land availability, and accounts for advances in agriculture productivity. However, other factors such as quality of life, environmental degradation, per capita income, etc. can also be used to arrive at an upper bound. The model holds good promise for usage for other developing countries.