What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

Answer: Option C

Let the principal be P and rate of interest be R%.
Therefore Required ratio
$$\begin{array}{rl}& =\frac{\frac{P\times R\times 6}{100}}{\frac{P\times R\times 9}{100}}\\ & =\frac{6PR}{6PR}\\ & =\frac{6}{9}\\ & =2:3\end{array}$$