A sum of money at a certain rate per annum of simple interest doubles in the 5 years and at a different rate becomes three times in 12 years. The lower rate of interest per annum is = ?

Answer: Option D

Rate of interest
$$=\frac{100(x-1)}{t}\%$$
Where x is the no. of times the sum becomes of itself. Here the sum is getting 3 times.
Therefore, x = 3
Where t is the time taken by sum to become x times of itself. Here, t = 12 years
By the short trick approach, we get
$$\begin{array}{rl}& =\frac{100(3-1)}{12}\\ & =\frac{200}{12}\\ & =\frac{50}{3}=16\frac{2}{3}\%\end{array}$$

Alternative Method :
Let the principal be P and in the 2nd scenario, SI = 2P
$$\begin{array}{rl}& \text{Rate}=\frac{\text{SI}\times 100}{\text{Principal}\times \text{Time}}\\ & =\frac{2\text{P}\times 100}{\text{P}\times 12}\\ & =\frac{50}{3}\\ & =16\frac{2}{3}\%\end{array}$$