The question in the image is written in Hindi and involves finding the value of $P$ based on an investment problem involving simple and compound interest.

Translation of the Problem:

A person invested two amounts, $2P$ rupees and $P$ rupees, at two different rates:

• $2P$ rupees at 8% compound interest (compounded annually)
• $P$ rupees at 15% simple interest for 2 years.

After two years, the difference between the compound interest and the simple interest earned is ₹410. You are required to find the value of $P$.

Solution Approach:

1. Simple Interest (SI) on $P$ at 15% for 2 years: $\text{SI} = \frac{P \times 15 \times 2}{100} = 0.3P$

2. Compound Interest (CI) on $2P$ at 8% for 2 years: The formula for compound interest is: $\text{CI} = 2P \left[ \left( 1 + \frac{8}{100} \right)^2 - 1 \right]$ Simplifying: $\text{CI} = 2P \left[ \left( 1 + 0.08 \right)^2 - 1 \right] = 2P \left( 1.1664 - 1 \right) = 2P \times 0.1664 = 0.3328P$

3. Difference between Compound Interest and Simple Interest: According to the question, the difference is ₹410: $0.3328P - 0.3P = 410$ Simplifying: $0.0328P = 410$ $P = \frac{410}{0.0328} = 12500$

Thus, the value of $P$ is ₹12,500.

Final Answer:

The correct option is A) 12,500.

Would you like further details on this solution? Here are some related questions for practice:

1. How would the result change if the interest rates were different?
2. What is the total amount of compound interest earned after 2 years?
3. How would the time period affect the difference between simple and compound interest?
4. What would the formula be for compound interest compounded monthly?
5. How can this method be applied to different types of investment problems?

Tip: Always ensure to distinguish between simple and compound interest formulas when solving problems like these, as their growth patterns differ significantly.