A person repays Rs 22500 after 10 years of borrowing a loan at 10% per annum simple interest. Using the relationship between amount, principal, rate, and time under simple interest, find the original loan amount that was borrowed.

Introduction / Context:
This problem asks us to find the original loan amount when the final amount repaid after a certain time at simple interest is known. The loan runs for 10 years at 10% per annum simple interest, and the borrower repays Rs 22500 in total. The candidate must express the amount in terms of the principal and simple interest, relate the interest to the principal using the simple interest formula, and then solve for the principal. This kind of question is standard in loan and banking based aptitude topics.

Given Data / Assumptions:

• Final amount repaid A = Rs 22500.
• Rate of simple interest R = 10% per annum.
• Time period T = 10 years.
• Original loan amount or principal P is unknown.
• Interest is calculated using simple interest throughout the 10 years.

Concept / Approach:
For simple interest, the interest earned or paid is:
SI = (P * R * T) / 100 The final amount A is:
A = P + SI Substituting the expression for SI, we have:
A = P + (P * R * T) / 100 = P * (1 + (R * T) / 100) Since A, R, and T are known, we can compute the factor multiplying P and then solve for P by dividing the amount by this factor.

Step-by-Step Solution:
Given A = Rs 22500, R = 10% per annum, T = 10 years. Compute the multiplier: 1 + (R * T) / 100. R * T = 10 * 10 = 100. (R * T) / 100 = 100 / 100 = 1. So the multiplier is 1 + 1 = 2. Therefore, A = P * 2. 22500 = 2P. P = 22500 / 2. P = 11250. Thus, the original loan amount borrowed was Rs 11250.

Verification / Alternative check:
We can verify by calculating the simple interest on Rs 11250 at 10% per annum for 10 years. SI = (11250 * 10 * 10) / 100. First compute 10 * 10 = 100, so SI = (11250 * 100) / 100 = 11250. The final amount A = P + SI = 11250 + 11250 = 22500, which matches the given amount repaid. This confirms that the original principal is Rs 11250.

Why Other Options Are Wrong:
If P were Rs 11225, the amount at 10% for 10 years would be 11225 * 2 = 22450, which is less than 22500.
If P were Rs 10000, the final amount would be 20000, too small.
If P were Rs 7500, the amount would be 15000, much smaller than 22500.
If P were Rs 12000, the amount would be 24000, which is more than 22500. Only Rs 11250 produces the correct final repayment amount under simple interest at 10% for 10 years.

Common Pitfalls:
Students sometimes confuse amount with interest and might try to treat Rs 22500 as interest instead of the total amount. Another error is to miscalculate the multiplier 1 + (R * T) / 100, especially for large time periods. Some candidates also forget that with 10% for 10 years, the simple interest equals the principal, doubling the amount. Recognizing that pattern can speed up calculations and reduce mistakes.

Final Answer:
The original loan amount borrowed by the person is Rs 11,250.