The simple interest on a certain deposit at 4.5% per annum is Rs 202.50 in one year. How much additional interest will the same deposit earn in one year if the rate is increased to 5% per annum while keeping the principal and time the same?

Introduction / Context: This question focuses on how the simple interest changes when the rate of interest increases while the principal and time remain the same. It is a quick calculation problem that shows that the additional interest depends only on the increase in rate, the principal, and the time period, not on the old rate itself.

Given Data / Assumptions:

Interest at 4.5% per annum for 1 year is Rs 202.50. Principal P is the same in both scenarios and is unknown initially. New rate of interest = 5% per annum. Time T = 1 year in both cases. Simple interest formula: SI = (P * R * T) / 100. We must find the additional interest in one year when the rate rises from 4.5% to 5% per annum.

Concept / Approach: First, we determine the principal from the given interest at 4.5% for one year. Once we know P, the extra interest due to the 0.5% rate increase is simply the interest at an additional 0.5% on that principal for 1 year. We can then compare the result with the options.

Step-by-Step Solution: Step 1: Use SI = (P * R * T) / 100 with SI = 202.50, R = 4.5, T = 1. Step 2: 202.50 = (P * 4.5 * 1) / 100. Step 3: Multiply both sides by 100: 20250 = 4.5P. Step 4: Therefore, P = 20250 / 4.5 = 4500. Step 5: Increase in rate = 5% - 4.5% = 0.5%. Step 6: Extra interest for 1 year at 0.5% = (P * 0.5 * 1) / 100. Step 7: Substitute P = 4500: Extra SI = (4500 * 0.5) / 100 = 2250 / 100 = 22.5. Step 8: Hence, the additional interest is Rs 22.50.

Verification / Alternative check: Compute interest at 5% directly and subtract the interest at 4.5%. At 5%, SI_new = (4500 * 5 * 1) / 100 = 225. At 4.5%, SI_old = 202.5. Difference = 225 - 202.5 = 22.5, which matches our earlier result.

Why Other Options Are Wrong: Rs 2.50 and Rs 20 correspond to much smaller increments than 0.5% on Rs 4500. Rs 25 is slightly larger than the correct difference, and Rs 202.50 represents the full interest at 4.5%, not the extra part. Only Rs 22.50 matches the correct increase in interest.

Common Pitfalls: Students sometimes wrongly compute the extra interest as 0.5% of the interest instead of 0.5% of the principal. Another error is to misinterpret the percentage step from 4.5 to 5 as a much larger relative increase. Always apply the changed rate directly to the principal when dealing with simple interest differences.

Final Answer: The deposit will earn an additional interest of Rs 22.50 in one year at 5% compared to 4.5%.