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 =
a) 5%
b) $$6\frac{2}{3}$$ %
c) 6%
d) $$7\frac{1}{5}$$ %

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