The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

${\left({\mathrm{T}}_{1/2}\right)}_{\mathrm{x}}={\left({\mathrm{t}}_{mean}\right)}_{\mathrm{y}}\Rightarrow \frac{0.693}{{\mathrm{\lambda }}_{\mathrm{x}}}=\frac{1}{{\mathrm{\lambda }}_{\mathrm{y}}}\Rightarrow {\mathrm{\lambda }}_{\mathrm{x}}=0.693{\mathrm{\lambda }}_{\mathrm{y}} \mathrm{or} {\mathrm{\lambda }}_{\mathrm{x}}<{\mathrm{\lambda }}_{\mathrm{y}}$ Also rate of decay = $\mathrm{\lambda N}$
Initially number of atoms (N) of both are equal but since ${\mathrm{\lambda }}_{\mathrm{y}}>{\mathrm{\lambda }}_{\mathrm{x}}$ , therefore, y will decay at a faster rate than x.