A sum of money becomes 16 5 times of itself in 22 years at r p.a. simple interest what is value of R

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let principal = P}} \cr & \therefore {\text{amount = 3P}} \cr & {\text{Interest = 3P}} - {\text{P}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 2P}} \cr & {\text{According to the question,}} \cr & {\text{2P = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{20}}}}{{100}} \cr & \Rightarrow {\text{R = 10% }} \cr} $$
Let after t years it will become double
$$\eqalign{ & {\text{Hence,}} \cr & {\text{Interest = 2P}} - {\text{P = P}} \cr & \Rightarrow {\text{P = }}\frac{{{\text{P}} \times 10 \times {\text{t}}}}{{100}} \cr & \Rightarrow {\text{t = 10 years}} \cr} $$