The simple interest on a sum of money is $$\frac{4}{9}$$ of the principal and the number of years is equal to the rate percent per annum. The rate per annum is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let the principal}} \cr & {\text{ = 9 units }} \cr & {\text{Hence simple interest}} \cr & {\text{ = }}\frac{4}{9} \times {\text{9 = 4 units}} \cr & {\text{Let,}} \cr & {\text{Rate of interest = R% }} \cr & {\text{R = T (given)}} \cr & {\text{By using formula}} \cr & \boxed{{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & 4 = \frac{{9 \times {\text{R}} \times {\text{R}}}}{{100}} \cr & {{\text{R}}^2} = \frac{{400}}{9} \cr & {\text{R = }}\frac{{20}}{3} = 6\frac{2}{3}\% \cr} $$