A person repays Rs. 22500 after 10 years of borrowing a loan at 10% per annum simple interest. Find the original loan amount that was borrowed.

Introduction / Context:
This is a typical loan repayment question under simple interest. The total amount repaid after a certain number of years and the rate of interest are given, and we must find the initial principal. Under simple interest, the amount increases linearly over time. This problem helps reinforce the relationship between principal, interest, rate, and time, and shows how to recover the principal from a known final amount.

Given Data / Assumptions:
Total amount repaid A after 10 years is Rs. 22500.
Rate of interest r is 10 percent per annum simple interest.
Time period t is 10 years.
Principal P is unknown and must be determined.
Interest is computed as simple interest throughout the loan period.

Concept / Approach:
Under simple interest, interest I is given by I = P * r * t / 100, and the amount A is A = P + I. Combining these yields A = P * (1 + r * t / 100). Knowing A, r, and t, we can solve for P by dividing A by the growth factor (1 + r * t / 100). Once P is found, we may cross check by computing the simple interest and amount again.

Step-by-Step Solution:
Write the formula for amount under simple interest: A = P * (1 + r * t / 100).Substitute A = 22500, r = 10, and t = 10.Compute r * t / 100 = 10 * 10 / 100 = 100 / 100 = 1.So A = P * (1 + 1) = P * 2.Thus 22500 = 2P.Solve for P by dividing both sides by 2: P = 22500 / 2 = 11250 rupees.Therefore the original loan amount borrowed was Rs. 11,250.

Verification / Alternative check:
For P = 11250, simple interest for 10 years at 10 percent is I = 11250 * 10 * 10 / 100 = 11250 * 100 / 100 = 11250 rupees. The total amount A is principal plus interest, which is 11250 + 11250 = 22500 rupees. This matches the amount repaid in the question, confirming that the initial loan was 11250 rupees.

Why Other Options Are Wrong:
If the principal had been Rs. 11,225, the amount after 10 years would be 11225 * 2 = 22450 rupees, which is less than 22500.
Rs. 10,000 as principal would lead to an amount of 20000 rupees, far below 22500.
Rs. 7,500 leads to only 15000 rupees after 10 years at the given rate.
Rs. 12,000 leads to 24000 rupees, which is more than the stated repayment. Therefore these values do not fit the given final amount.

Common Pitfalls:
Some learners forget that at 10 percent per annum for 10 years, the total interest is equal to the principal, meaning the amount doubles. Others incorrectly apply compound interest reasoning or miscalculate the factor 1 + r * t / 100. Clearly recognizing that simple interest adds a fixed percentage of the principal each year makes the doubling effect easy to see and avoids confusion.

Final Answer:
The loan amount originally borrowed at 10 percent simple interest per annum was Rs. 11,250.