A sum of money becomes $$\frac{7}{6}$$ of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is ?
a) $$5\frac{5}{9}$$ %
b) $$6\frac{5}{9}$$ %
c) 18 %
d) 25 %

Answer: a
Explanation:
$$\eqalign{ & {\text{Let principal = 6P}} \cr & {\text{Hence Amount}} \cr & {\text{ = 6P}} \times \frac{7}{6} = 7{\text{P}} \cr & {\text{SI = 7P}} – {\text{6P = P}} \cr & {\text{Time = 3 years}} \cr & {{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & {\text{P = }}\frac{{6{\text{P}} \times {\text{R}} \times {\text{3}}}}{{100}} \cr & {\text{R = }}\frac{{100}}{{18}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{50}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 5\frac{5}{9}\% \cr} $$