The half life of an element A is equal to the mean life of an element B. If, initially (i.e., at t = 0), A and B have equal number of radioactive nuclei, then:

Half life $T=\frac{\ln \left(2\right)}{\lambda }$

Mean life $\tau =\frac{1}{\lambda }$. Therefore,

$T=\tau \ln \left(2\right)$

$T_A={\tau }_A\ln \left(2\right)$

$T_B={\tau }_B\ln \left(2\right)$

Given $T_A={\tau }_{B.}$Hence, 

$\frac{T_B}{T_A}=\ln \left(2\right)=0.693$

So $T_B<T_A$, which implies ${\lambda }_B>{\lambda }_A$

Since $\frac{dN}{dt}=-\lambda N$

$\frac{d{N}_A}{dt}=-{\lambda }_A{N}_A$

$\frac{d{N}_B}{dt}=-{\lambda }_B{N}_B$             

Given, initially, $N_A=N_{B.}$Hence 

$\frac{{\displaystyle \frac{d{N}_A}{dt}}}{{\displaystyle \frac{d{N}_B}{dt}}}=\frac{{\lambda }_A}{{\lambda }_B}<1$

or  $\frac{d{N}_B}{dt}>\frac{d{N}_A}{dt}$

Hence B decays at a faster rate than A.