Consider two radioactive substances $\mathbf{P}$ and $\mathbf{Q}$ that decay following a first order kinetics. It takes nine years for $\mathbf{P}$ for decay of $2 / 3^{\text {rd }}$ of its initial amount. In the same nine years $\mathbf{Q}$ decays by half. If the ratio of the initial $(t=0)$ amounts of $\mathbf{P}$ and $\mathbf{Q}$, that is $\mathbf{P}_0: \mathbf{Q}_0$ is $81: 16$, the number of years after which the quantities of $\mathbf{P}$ and $\mathbf{Q}$ would be same is

• Correct answer
  A

  36
• B

  9
• C

  54
• D

  72

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