What is the rate of interest per cent?
I. An amount doubles itself in 5 years on simple interest.
II. Difference between the compound interest and the simple interest earned on a certain amount in two years is Rs. 400.
III. Simple interest earned per annum is Rs. 2,000.

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

Statement I : Let Principal = Rs. $$x$$

=> Amount after 5 years = Rs. $$2x$$

=> Interest after 5 years = Rs. $$(2x - x) = x$$

$$\therefore$$ S.I. = $$\frac{P \times R \times T}{100}$$

=> $$x = \frac{x \times r \times 5}{100}$$

=> $$r = \frac{100}{5} = 20 \%$$

Thus, I alone is sufficient.

Statement II : C.I. - S.I. = 400

=> $$(P [(1 + \frac{r}{100})^2 - 1]) - (\frac{P \times r \times 2}{100}) = 400$$ -----------Eqn(1)

Here, 2 variables (P & r) are unknown. So, II alone is insufficient.

Combining II and III : 

S.I. earned for 1 year = Rs. 2000

=> $$\frac{P \times r \times 1}{100} = 2000$$

=> $$P \times r = 2,00,000$$

Substituting above value in equation (1), we get $$r = 20 \%$$

Thus, II and III together are sufficient.