We have performed detailed high-resolution spectroscopic analysis on seven metal-poor stars (BD+75348, BD+093019, HD238020, HE0319-0215, HE0507-1653, HE0930-0018, HE1023-1504) and derived their atmospheric parameters Teff, logg, [Fe/H], and microturbulent velocity ({xi}). The metallicity range is found to be -2.57<[Fe/H]<-0.42. The elemental abundances of 17 light elements and 12 heavy elements are estimated. We have classified BD+75348 and BD+093019 as strong Ba stars, HD238020 as a mild Ba star, and the remaining four objects as CEMP-s stars. We have estimated the masses of the stars from Hertzsprung-Russel (HR) diagram, and, compiling the data of 205 Ba stars from literature, estimated the mass distribution of Ba stars. We have also estimated the initial masses of the companion AGBs of the program stars as well as the masses of the companion AGBs of 159 Ba and 36 CEMP-s stars from literature, with the help of a parametric-model-based analysis using FRUITY models. While the primary mass distribution of mild Ba stars peaks at 3.7M{sun}, for the strong Ba stars the peak appears at 2.5M{sun}. We, therefore, propose that the initial masses of the progenitor AGBs dominantly control the formation of mild and strong Ba stars. However, a clear overlap, in the range 1.3-4.0M{sun}, noticed between the progenitor masses of both the subclasses of Ba stars, may indicate that other factors, such as the metallicities and the orbital periods, may also have significant contributions. The progenitor AGBs' mass distribution of CEMP-s stars is found to peak at 2.03M{sun}.