The simple and compound interest that can be earned in two years at the same rate is Rs 1,000 and Rs 1,040 respectively. What is the rate (percent per annum) of interest?

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

Time period = 2 years

Simple interest = $$\frac{P\times r \times t}{100}$$

=> $$\frac{100x\times r \times2}{100}=1000$$

=> $$2rx=1000$$

=> $$x=\frac{1000}{2r}=\frac{500}{r}$$

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

=> $$100x[(1+\frac{r}{100})^2-1]=1040$$

=> $$\frac{100 \times500}{r}[1+\frac{r^2}{10000}+\frac{2r}{100}-1]=1040$$

=> $$\frac{50000}{r} \times (\frac{r^2}{10000}+\frac{2r}{100})=1040$$

=> $$5r+1000=1040$$

=> $$5r=1040-1000=40$$

=> $$r=\frac{40}{5}=8\%$$

=> Ans - (C)