A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double itself at the same rate of simple interest ?

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