  In the present work, we analyze several strange as well as non-strange
relative hadronic yields obtained in the ultra-relativistic heavy-ion
collisions (URHIC) experiments over a wide range of centre-of-mass collision
energy ($\sqrt{s_{NN}}$). We invoke the formation of a hot and dense hadronic
resonance gas (HRG) in the final stage following the URHIC. We use an earlier
proposed thermodynamically consistent approach for obtaining the equation of
state (EoS) of a HRG. It takes into account an important aspect of the hadronic
interaction, viz., the hadronic hard-core repulsion, by assigning hard-core
volumes to the hadrons, leading to an excluded volume (EV) type effect. We have
invoked the bag model approach to assign hard-core volumes to baryons
(antibaryons) while treating mesons to be point particles. We employ ansatz to
obtain the dependence of the temperature and BCP of the HRG system on the
centre-of-mass energy in the URHIC. We also find strong evidence of double
freeze-out scenario, corresponding to baryons (antibaryons) and mesons,
respectively. Strangeness (anti-strangeness) imbalance factor is also seen to
play an important role in explaining the ratio of strange hadrons to the
non-strange ones. The HRG model can explain the experimental data on various
relative hadronic multiplicities quite satisfactorily over a wide range of
$\sqrt{s_{NN}}$, ranging from the lowest RHIC energies to the highest LHC
energies for the set of the model parameters obtaining the best theoretical fit
to the experimental data by minimizing the $\chi^{2}$/dof value.
