A certain sum of money earns a simple interest of ₹ 800 over 2-year period. The same sum of money invested at the same rate of interest and same period on a compound interest basis earns an interest of ₹ 900. What is the sum?

Let the amount invested be 'P' and the rate of interest be 'r'.

Simple interest =$$\ \frac{\ P\times r\times2}{100}$$, which is equal to 800

=> $$\frac{\Pr}{100}=400$$

Compound interest = $$P\left(1+\frac{r}{100}\right)^2-P\ $$ = 900

$$P\left(\frac{r}{100}\right)^2+\frac{2\Pr}{100}=900$$

$$P\left(\frac{r}{100}\right)^2=100$$

$$400\left(\frac{r}{100}\right)=100$$

r = 25%

P = $$\frac{400\left(100\right)}{25}$$ = Rs 1600

The answer is option B.