The difference between the compound interest and simple interest accrued on a principal amount over 2 years at a rate of 15% per annum is Rs. 135. Find the principal sum.

The correct answer is Rs. 6,000.

Given Data:
Difference between Compound Interest (CI) and Simple Interest (SI) for 2 years = Rs. 135
Rate of interest ($r$) = 15% per annum
Time period ($t$) = 2 years

Formula:
The difference between Compound Interest and Simple Interest accrued on a principal amount over 2 years is given by:

$\text{Difference}=P\times {\left(\frac{r}{100}\right)}^2$

where $P$ represents the principal sum and $r$ is the annual rate of interest.

Step-by-step Solution:

Substitute the given values into the formula:

$135=P\times {\left(\frac{15}{100}\right)}^2$

Simplify the fraction $\frac{15}{100}$ to $\frac{3}{20}$:

$135=P\times {\left(\frac{3}{20}\right)}^2$

Square the fraction $\frac{3}{20}$:

$135=P\times \frac{9}{400}$

Rearrange the terms to solve for $P$:

$P=\frac{135\times 400}{9}$

Divide 135 by 9:

$P=15\times 400$

$P=6000$

Thus, the principal sum is Rs. 6,000.