Simple Interest — Two banks and a small rate gap: On a principal of ₹ 500 kept for a period of 2 years, the difference between the simple interest earned from two different banks is ₹ 2.50. What is the difference between their annual rates of interest (in percentage points)?

Introduction / Context:
When two banks offer slightly different simple interest (SI) rates on the same principal for the same time, the difference in interest directly reveals the difference in their annual percentage rates. This question tests the SI formula and unit handling for small percentage gaps.

Given Data / Assumptions:

• Principal P = ₹ 500
• Time t = 2 years
• Difference in simple interest ΔI = ₹ 2.50
• Let rate difference = Δr (in % per annum)

Concept / Approach:
Simple interest is I = (P * r * t) / 100. For the same P and t, the interest difference equals (P * Δr * t)/100. Solve for Δr.

Step-by-Step Solution:
ΔI = (P * Δr * t) / 1002.50 = (500 * Δr * 2) / 1002.50 = (1000 * Δr) / 1002.50 = 10 * ΔrΔr = 2.50 / 10 = 0.25%

Verification / Alternative check:
If Bank A is r% and Bank B is (r + 0.25)%, the annual gap on ₹ 500 is 500 * 0.25 / 100 = ₹ 1.25. Over 2 years the gap is ₹ 2.50, matching the data.

Why Other Options Are Wrong:
1% and 2.50% would produce much larger gaps; 0.50% doubles the required difference; 0.75% is also too large relative to ₹ 2.50 over 2 years.

Common Pitfalls:
Confusing the percentage gap with rupees, forgetting to divide by 100, or using 2.50 as a percent rather than rupees can lead to mistakes.

Final Answer:
0.25%