Difficulty: Easy
Correct Answer: Rs. 1625
Explanation:
Introduction / Context:
This problem asks you to find the principal when the final amount, simple interest rate, and time are known. The rate is given as 13 1/2% per annum, which is a mixed fraction and must be converted properly into a decimal or an equivalent percentage.
Given Data / Assumptions:
Concept / Approach:
For simple interest, the amount A is given by A = P + SI, and SI = (P * R * T) / 100. Combining these, A = P * (1 + R * T / 100). Since A, R, and T are known, you can solve for P by dividing the amount by the factor (1 + R * T / 100).
Step-by-Step Solution:
Step 1: Convert the rate 13 1/2% into decimal form: 13 1/2% = 13.5%.
Step 2: Compute R * T / 100. Here, R = 13.5 and T = 4, so R * T / 100 = (13.5 * 4) / 100.
Step 3: Calculate 13.5 * 4 = 54, so R * T / 100 = 54 / 100 = 0.54.
Step 4: Amount formula: A = P * (1 + 0.54) = P * 1.54.
Step 5: Given A = Rs. 2502.50, so 2502.50 = P * 1.54.
Step 6: Solve for P: P = 2502.50 / 1.54 = Rs. 1625.
Verification / Alternative check:
To verify, calculate the simple interest on Rs. 1625 at 13.5% for 4 years. SI = (1625 * 13.5 * 4) / 100. First, 1625 * 13.5 = 21937.5. Then 21937.5 * 4 = 87750. Finally, 87750 / 100 = 877.50. Add this to the principal: 1625 + 877.50 = 2502.50, which matches the given amount.
Why Other Options Are Wrong:
Rs. 1525, Rs. 1425, and Rs. 1325 would all produce final amounts different from Rs. 2502.50 when you apply the same rate and time. Each would result in a smaller amount because the principal is lower than the correct value.
Common Pitfalls:
Students sometimes misread 13 1/2% as 13.2% or treat it as 13.12%, which is incorrect. Others forget to convert the percentage properly or make mistakes when applying the amount formula. Keeping track of the multiplication and division steps carefully avoids such errors.
Final Answer:
The original principal sum is Rs. 1625.
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