A person lends a certain sum of money at 10% per annum simple interest. After 20 years, the total interest earned is Rs. 500 more than the original principal lent. What was the principal amount (in rupees) that was lent?

Introduction / Context:
This question checks your understanding of the relationship between principal, rate, time, and simple interest when you know that the interest itself exceeds the principal by a certain fixed amount. The rate of 10% per annum and a long time period of 20 years make the simple interest a multiple of the principal. Using this information, plus the condition that the interest is Rs. 500 more than the principal, we can set up a simple equation to find the original sum that was lent.

Given Data / Assumptions:

• Rate of interest R = 10% per annum (simple interest).
• Time T = 20 years.
• The total simple interest earned after 20 years is Rs. 500 more than the principal.
• We assume a fixed rate over the entire period with no partial withdrawals.

Concept / Approach:
For simple interest, SI = P * R * T / 100. At 10% per annum for 20 years, SI becomes SI = P * 10 * 20 / 100 = 2P. The question states that this simple interest is Rs. 500 more than the principal amount. Therefore, we can equate SI = P + 500. Substituting SI = 2P into that relationship allows us to solve for P. Once P is known, we can confirm that the interest calculated indeed exceeds it by Rs. 500, which validates our result.

Step-by-Step Solution:
Step 1: Let the principal be P rupees. Step 2: Simple interest formula: SI = P * R * T / 100. Step 3: Substitute R = 10% and T = 20 years: SI = P * 10 * 20 / 100 = 2P. Step 4: According to the question, the interest is Rs. 500 more than the principal, so SI = P + 500. Step 5: Equate the two expressions for SI: 2P = P + 500. Step 6: Subtract P from both sides: 2P - P = 500, so P = 500. Step 7: Therefore, the principal amount lent is Rs. 500.

Verification / Alternative check:
Verify the result by computing the interest on P = 500. Simple interest at 10% per annum for 20 years is SI = 500 * 10 * 20 / 100 = 500 * 2 = 1000 rupees. Compare SI with P: SI = 1000, P = 500, and SI - P = 1000 - 500 = 500 rupees. This difference exactly matches the given statement that the interest is Rs. 500 more than the sum lent, confirming that P = 500 is correct.

Why Other Options Are Wrong:
If P = 200, the interest would be 200 * 10 * 20 / 100 = 400, so SI - P = 200, not 500. For P = 1000, SI would be 2000 and the difference would be 1000. For P = 250, SI would be 500 and the difference SI - P would be only 250. None of these match the required excess of Rs. 500 over the principal, so those options are incorrect.

Common Pitfalls:
A frequent error is to interpret the statement as describing the total amount (principal plus interest) instead of just the interest. Another common mistake is to miscalculate the simple interest for a long duration, forgetting that time is 20 years. Some students also attempt to guess the principal using rough mental calculations without forming an equation, which can easily lead to off-by-one errors. Always translate unusual wording like “interest amounted to Rs. 500 more than the sum lent” into a clear algebraic statement before solving.

Final Answer:
The principal amount lent at 10% simple interest is Rs. 500.