Explanation:

To solve this, we will use the compound interest formula:

$$A=P(1+r{)}^n$$

- Initial Scenario:

- Amount after 6 years: Rs. 25,000

- Amount after 12 years: Rs. 40,000

- These are compounded annually.

- Step-by-Step Analysis:

- For 6 to 12 years (6 additional years), Rs. 25,000 grows to Rs. 40,000.

- Compound interest formula: $$40,000=25,000\times (1+r{)}^6$$

- Solving for $(1+r{)}^6=\frac{40,000}{25,000}=1.6$

- Original principal:

$$25,000=P(1.6)=P(1+r{)}^6$$

- Finding the correct Initial Amount:

- Apply backward by dividing 25,000 by $(1+r{)}^6$.

- Assume various option values and backtrack calculations.

- Checking Options:

- Option 1: Rs. 12,325

- Option 2: Rs. 14,645

- Option 3: Rs. 15,625 ()

- Option 4: Rs. 13,725

- Option 5: None of these

- Correct Answer Process:

- By solving with relevant calculations among the options.

- Option 3: Rs. 15,625 suits the back-cast values due to correct proportions when compound increase pairs are balanced at expected rates of growth needed for Rs. 25,000 & Rs. 40,000.

Your Correct Answer:

- Option 3: Rs. 15,625