The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23 : 7 respectively. What is rate of interest per annum (in %)?

Let rate of interest = $$r\%$$

Difference between compound interest and simple interest on Rs. $$P$$ for 2 years = $$P(\frac{r}{100})^2$$

Difference for 3 years = $$P(\frac{r}{100})^2(\frac{r}{100}+3)$$

According to ques,

=> $$P(\frac{r}{100})^2(\frac{r}{100}+3):P(\frac{r}{100})^2=23:7$$

=> $$\frac{(\frac{r}{100}+3)}{1}=\frac{23}{7}$$

=> $$7(\frac{r}{100}+3)=23$$

=> $$\frac{7r}{100}+21=23$$

=> $$\frac{7r}{100}=23-21=2$$

=> $$r=\frac{100}{7}\times2=\frac{200}{7}\%$$

=> Ans - (A)