A sum of money becomes ₹13,380 after 3 years and ₹20,070 after 6 years on compound Interest. Find the sum?

Let us assume that the interest rate is r. And the principal amount is P. 
The sum after three years would be, $$P\left(1+\frac{r}{100}\right)^3$$, we are told that this value is 13380. 

Similarly, the sum after six years would be, $$P\left(1+\frac{r}{100}\right)^6$$, we are told that this value is 20,070. 

Let us divide the latter by the former, we get, 

$$\frac{P\left(1+\frac{r}{100}\right)^6}{P\left(1+\frac{r}{100}\right)^3}=\frac{20070}{13380}=1.5$$

Therefore, $$\left(1+\frac{r}{100}\right)^3=1.5$$

Substituting this value in the first equation we have, $$P\left(1.5\right)=13380$$

We get P = 8920. 

Hence, the answer is Option D.