Half life of a radioactive substance A is two times the half life of another radioactive substance B. Initially the number of nuclei of A and B are $N_{A}and{N}_B$ respectively. After three half lives of A number of nuclei of both are equal. Then the ratio $N_A/N_B$ is

Let's denote the half-life of substance B as "t" (in any time unit) and the half-life of substance A as "2t".

The amount remaining after n half-lives is,

$N=N_0{\left(\frac{1}{2}\right)}^n$

Now the remaining amount of $A=N_A{\left(\frac{1}{2}\right)}^3$

Reaming amount of $B=N_B{\left(\frac{1}{2}\right)}^6$

Simplifying, we get:

$N_A{\left(\frac{1}{2}\right)}^3=N_B{\left(\frac{1}{2}\right)}^6$

$\frac{N_A}{N_B}=\frac{1}{8}$

Hence the correct answer is $\frac{1}{8}.$