Explanation:

- Simple Interest for Rachit:

- Formula: $SI=\frac{P\times R\times T}{100}$.

- For Rachit: $SI=\frac{12000\times R\times 2}{100}$.

- The total interest for 2 years is $240R$.

- Compound Interest for Prasad:

- Formula: $CI=P\times {(1+\frac{R}{100})}^T-P$.

- For Prasad: $CI=12000\times {(1+\frac{R}{100})}^2-12000$.

- Difference in Interest:

- Given: $\text{Difference}=Rs172.80$.

- Equation: $12000\times {(1+\frac{R}{100})}^2-12000-240R=172.8$.

- Calculation to find $R$:

- Solving the above equation, we find $R$.

- Options:

- 10%

- 8%

- 12% (This is the value that satisfies the equation)

- 5%