Explanation:

To solve the problem, we need to calculate the interest under both annual and half-yearly compounding methods.

- Annual Compounding:

- Let the principal amount be \( P \).

- The formula for compound interest annually is:

$$

\text{Amount} = P \times \left(1 + \frac{10}{100}\right)^1 = P \times 1.1

$$

- Interest = \( P \times 1.1 - P = 0.1P \).

- Half-Yearly Compounding:

- With half-yearly compounding, the rate for each half-year is 5% (i.e., 10%/2).

- The formula is:

$$

\text{Amount} = P \times \left(1 + \frac{5}{100}\right)^2 = P \times 1.1025

$$

- Interest = \( P \times 1.1025 - P = 0.1025P \).

- Interest Difference:

- Difference in interest = \( 0.1025P - 0.1P = 0.0025P \).

- We know the difference is Rs. 80, so \( 0.0025P = 80 \).

- Solving for \( P \):

$$

P = \frac{80}{0.0025} = 32000

$$

- Conclusion:

- Correct Answer: Option 2 - 32000