The simple and compound interest that can be earned in two years at the same rate is Rs 1500 and Rs 1575 respectively. What is the rate (% per annum) of interest?

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

Time period = 2 years

Simple Interest = $$\frac{P \times R \times T}{100} = 1500$$

=> $$\frac{100x \times r \times 2}{100} = 1500$$

=> $$2rx = 1500$$

=> $$x = \frac{1500}{2r} = \frac{750}{r}$$

Compound Interest = $$P [(1 + \frac{R}{100})^T - 1] = 1575$$

=> $$100x [(1 + \frac{r}{100})^2 - 1] = 1575$$

=> $$100x [(1 + \frac{r^2}{100^2} + 2\frac{r}{100}) - 1] = 1575$$

=> $$(100 \times \frac{750}{r}) [\frac{r^2}{10000} + \frac{2r}{100}] = 1575$$

=> $$7.5r + 1500 = 1575$$

=> $$7.5r = 1575 - 1500 = 75$$

=> $$r = \frac{75}{7.5} = 10 \%$$

=> Ans - (B)