Find ratio of number of atoms of $A$ and $B$
There are two radio nuclei A and B. A is α emitter and B is β 
  emitter and their decay constant are in ratio 1:2


So B decays twice as fast as A.  If we want the actual number of decay events from A to equal the actual number of decay events from B at t=0, then we must have twice as much A present as B at t=0.

We are given that $\ce{k_{B} = 2k_{A}}$. For the decay events at T=0 to be equal for A and B, then $$\ce{[B]_{o} * k_{B}~=~[A]_{o} * k_{A}}$$
$$\ce{[B]_{o} * 2k_{A}~=~[A]_{o} * k_{A}}$$
or $$\ce{\frac{2}{1}~=~\frac{[A]_{o}}{[B]_{o}}}$$
At t=0, the concentration of A must be twice the concentration of B in order for equal decay events to occur from A and B