A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is ?

Answer: Option A

$$\begin{array}{rl}& \text{Let principal = 6P}\\ & \text{Hence Amount}\\ & \text{ = 6P}\times \frac{7}{6}=7\text{P}\\ & \therefore \text{SI = 7P}-\text{6P = P}\\ & \text{Time = 3 years}\\ & \boxed{\text{SI = }\frac{\text{P}\times \text{T}\times \text{R}}{100}}\\ & \Rightarrow \text{P = }\frac{6\text{P}\times \text{R}\times \text{3}}{100}\\ & \Rightarrow \text{R = }\frac{100}{18}\\ & =\frac{50}{9}\\ & =5\frac{5}{9}\%\end{array}$$

Alternate:
Note: In such type of questions to save your valuable time try to think like that.
\begin{gathered} \begin{array}{*{20}{c}} {{\text{Amount}}}&{{\text{Principal}}} \end{array} \hfill \\ {\text{ }}\underbrace {7\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{6}}}_{ + 1} \hfill \\ \end{gathered}
\begin{aligned} & {\text{Required rate % }} \\ & {\text{ = }}\frac{1}{6} \times \frac{{100}}{3} \\ & = 5\frac{5}{9}\% \\\end{aligned}