On a certain sum, the Compound Interest and Simple Interest at some rate per cent are Rs.696.30 and Rs.660 respectively in 2 years. Find the sum.

Let say , sum is P and rate of interest is r %.

So, $$P\times2\times\frac{r}{100}=660.$$

So, $$\frac{\Pr}{100}=330.$$...............................(1)

And, $$P\left(1+\frac{r}{100}\right)^2-P=696.30$$

or,$$P\left(1+\frac{r^2}{100^2}+\frac{2r}{100}-1\right)=696.30$$

or, $$\frac{\Pr}{100}.\frac{r}{100}+\frac{2\Pr}{100}=696.30$$

or, $$330.\frac{r}{100}+2\times330=696.30$$

or, $$330.\frac{r}{100}=36.30$$

or, $$\frac{r}{100}=\frac{36.30}{330}=0.11$$

or, $$r=11.$$

Put this value in (1) :

$$\frac{11P}{100}=330$$

or, $$P=3000.$$

D is correct choice.