The compound interest on a certain sum of money at a certain rate per annum for two years is 2,050, and the simple interest on the same amount of money at the same rate for 3 years is 3, 000. Then the sum of money is

let the sum of money be Rs P

And rate of interest = R %

It is given that for two years the Compound Interest = Rs 2050

CI = $$P(1 + \frac{R}{100})^T - P$$

2050 = $$P((1 + \frac{R}{100})^2- 1)$$ .......(1)

As it is given that for 3 years the Simple Interest = Rs 3000 and we know that SI for every year is same so for 1st year

Simple interest = Rs 1000

For 1st year SI and CI are same if rate of interest and Principal amount is same and hence for 1st year CI = 1000

For 2 years the CI = 2050 = 1000 + 1000 + ($$\frac{R}{100}$$ \times 1000)

R = 5%

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

3000 = $$\frac{P \times 5 \times 3}{100}$$

P = Rs 20000