The half-life period of a radio-active element X is same as the mean life time of another radio-active element Y. Initially they have the same number of atoms.Then

According to question,Half life of $\mathrm{X},T_{1/2}={\tau }_{av},$ average life of Y  

$\Rightarrow \frac{0.693}{{\lambda }_x}=\frac{1}{{\lambda }_y}\Rightarrow {\lambda }_X=\left(0.693\right)\cdot {\lambda }_y\therefore {\lambda }_X<{\lambda }_Y$

 Now , the rate of decay is given by

$-{\left(\frac{dN}{dt}\right)}_x={\lambda }_x{N}_0;$

$-{\left(\frac{dN}{dt}\right)}_y={\lambda }_y{N}_0$

  Y will decay faster than X.