A sum amounts to ₹8,028 in 3 years and to ₹12,042 in 6 years at a certain rate percent per annum, when the interest is compounded yearly. The sum is:

Formula for Amount when compound interest is applied 

Amount= P $$\times (1 + \frac{r}{100})^n$$ 

where

P = Principal

r = Rate of Interest

n = Number of years

Let the Principal be Rs.x .

According to question ,

8,028 = x $$( 1 + \frac{r}{100} )^3$$ -------------- 1

12,042 = x $$( 1 + \frac{r}{100} )^6$$ --------------2

Dividing 2 by 1 , we get ,

1.5 = $$( 1 + \frac{r}{100} )^3$$

Using this value in 1 , we get ,

8,028 = x $$( 1 + \frac{r}{100} )^3$$

8,028 = x $$\times 1.5$$

x = 8028 /1.5 = 5352

So , the answer would be Option a) Rs 5352 .