Gopal borrowed a sum of money at 12% simple interest per annum. If he had to pay back Rs 1,280 after 5 years in order to clear the loan, what amount did he originally borrow as principal?

Introduction / Context:
This is a straightforward simple interest problem where the final amount after a given time period is known, and you must work backward to find the original principal. Such problems are common in banking aptitude tests and help you practice reversing the simple interest formula and understanding the relation between amount, principal, and interest.

Given Data / Assumptions:

Amount paid after 5 years, A = Rs 1,280.
Rate of interest R = 12% per annum (simple interest).
Time T = 5 years.
Principal P is unknown.
Simple interest SI = (P * R * T) / 100, and Amount A = P + SI.

Concept / Approach:
We first express the amount in terms of the principal using the simple interest formula. Because amount equals principal plus simple interest, we can write A = P * (1 + (R * T) / 100). Substituting the known values of A, R, and T results in a simple equation in one variable P, which we then solve to find the principal Gopal borrowed.

Step-by-Step Solution:
Step 1: Use the relationship A = P + SI where SI = (P * R * T) / 100. Step 2: Substitute R = 12 and T = 5 into SI: SI = (P * 12 * 5) / 100 = (P * 60) / 100 = 0.6P. Step 3: Therefore, A = P + 0.6P = 1.6P. Step 4: Given A = 1280, so 1.6P = 1280. Step 5: Solve for P by dividing both sides by 1.6: P = 1280 / 1.6. Step 6: 1280 / 1.6 = 800. Step 7: Hence, Gopal originally borrowed Rs 800.

Verification / Alternative check:
Compute the simple interest on Rs 800 at 12% for 5 years. SI = (800 * 12 * 5) / 100 = (800 * 60) / 100 = 480. Amount A = P + SI = 800 + 480 = 1280, which matches the given repayment amount. This confirms that the principal is correctly calculated as Rs 800.

Why Other Options Are Wrong:
If the principal were Rs 620, Rs 560, Rs 480, or Rs 700, the amount after 5 years at 12% simple interest would be different from Rs 1280. For example, for P = 700, interest would be (700 * 12 * 5) / 100 = 420 and amount would be 1120, not 1280. Thus, these options do not satisfy the given condition.

Common Pitfalls:
Some test takers compute only the interest and forget to add it to or subtract it from the amount appropriately when solving backward. Others may miscalculate the factor (1 + R * T / 100), or mistakenly use compound interest formulas. Always verify that the method aligns with simple interest and that the final amount is consistent with the given data.

Final Answer:
The original principal borrowed by Gopal is Rs 800.