The simple interest on a sum of money for 3 years is Rs. 240 and the compound interest on the same sum, at the same rate for 2 years is Rs. 170. The rate of interest is:

Let principal sum = Rs. $$100x$$ and rate of interest = $$r\%$$

Simple interest = $$\frac{P\times R\times T}{100}$$

=> $$\frac{100x\times r\times 3}{100}=240$$

=> $$3rx=240$$

=> $$x=\frac{240}{3r}=\frac{80}{r}$$

Compound interest = $$P[(1+\frac{R}{100})^T-1]$$

=> $$100x[(1+\frac{r}{100})^2-1]=170$$

=> $$(100\times\frac{80}{r})[(1+\frac{r}{100})^2-1]=170$$

=> $$\frac{800}{r}\times(1+\frac{r^2}{10000}+\frac{2r}{100}-1)=17$$

=> $$\frac{8r}{100}+16=17$$

=> $$\frac{8r}{100}=17-16=1$$

=> $$r=\frac{100}{8}=12\frac{1}{2}\%$$

=> Ans - (C)