The ratios of Bd and Bs meson decay constant have been estimated using the variational method in conjunction with the relativistic Hamiltonian of the heavy meson in the framework of the statistical model. The ratio of CKM matrix elements [Formula: see text] has been extracted from [Formula: see text] mixing using the estimated decay constants and ratio of Bd and Bs mass differences. The results are found to be in good agreement with the existing theoretical and experimental predictions.