Recently, our understanding of the origin of W UMa-type contact binaries has become clearer. Initial masses of their components were successfully estimated by Yildiz and Dogan using a new method mainly based on observational properties of overluminous secondary components. In this paper, we continue to discuss the results and make computations for age and orbital evolution of these binaries. It is shown that the secondary mass, according to its luminosity, also successfully predicts the observed radius. While the current mass of the primary component is determined by initial masses, the current secondary mass is also a function of initial angular momentum. We develop methods to compute the age of A- and W-subtype W UMa-type contact binaries in terms of initial masses and mass according to the luminosity of the secondaries. Comparisons of our results with the mean ages from kinematic properties of these binaries and data pertaining to contact binaries in open and globular clusters have increased our confidence on this method. The mean ages of both A- and W-subtype contact binaries are found as 4.4 and 4.6Gyr, respectively. From kinematic studies, these ages are given as 4.5 and 4.4Gyr, respectively. We also compute orbital properties of A-subtype contact binaries at the time of the first overflow. Initial angular momentum of these binaries is computed by comparing them with the well-known detached binaries. The angular momentum loss rate derived in the present study for the detached phase is in very good agreement with the semi-empirical rates available in the literature. In addition to the limitations on the initial masses of W UMa-type contact binaries, it is shown that the initial period of these binaries is less than about 4.45d.