Explanation:

- Problem: Identify the principal amount that results in a compound interest of Rs 1,522.50 over 2 years, with a 10% annual interest rate.

- Formula: Use the compound interest formula:

$$

A = P \left(1 + \frac{r}{100}\right)^n

$$

Here, \(A\) is the future value (principal + interest), \(P\) is the principal, \(r\) is the rate of interest, and \(n\) is the number of years.

- Calculation:

$$

\begin{align*}

A &= P \times \left(1.10\right)^2 \\

A &= P \times 1.21 \\

\text{Given, } A - P &= 1522.50 \\

P \times 1.21 - P &= 1522.50 \\

0.21P &= 1522.50 \\

P &= \frac{1522.50}{0.21} \\

P &= 7250 \\

\end{align*}

$$

- Option:1, Rs7,250: Matches the calculated principal.

- Option:2, Rs7,200: Does not match.

- Option:3, Rs7,500: Does not match.

- Option:4, Rs7,000: Does not match.

- Correct Answer: Option 1, Rs7,250.