Simple interest on a certain sum at a certain annual rate of interest is $$\frac{1}{9}$$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr} $$