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 $A$, the number of nuclei of both are equal. Then $\frac{\mathrm{N}_{\mathrm{A}}}{\mathrm{N}_{\mathrm{B}}}$ is

• A

  $\frac{1}{3}$
• B

  $\frac{1}{4}$
• C

  $\frac{1}{6}$
• Correct answer
  D

  $\frac{1}{8}$

Hence, the correct answer is option: 'D'.