We have used two calibration free laser induced breakdown spectroscopy (CF-LIBS) methods for the quantitative analysis of Pb-Sn alloys with different compositions. The first method is based on Boltzmann plots where the elemental concentration is determined from the intercept along the y-axis whereas the second method is the electron density conservation method, in which elemental compositions are determined by comparing the experimentally measured number density with the theoretical results obtained by CF-LIBS. The neutral spectral lines of lead and tin have been used for the estimation of plasma temperature by the Boltzmann plot method whereas the Saha-Boltzmann equation has been used to calculate the electron number density. By comparing the results of both CF-LIBS methods, it is concluded that the CF-LIBS (electron number density conservation) method is more appropriate than the CF-LIBS (Boltzmann plot method) for the quantitative elemental analysis.