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?

Let the principal be P and rate of interest be R%.

Required ratio = $\frac{\frac{P*R*6}{100}}{\frac{P*R*9}{100}}=\frac{6PR}{9PR}=\frac{6}{9}=\frac{2}{3}$