A sum of ₹2,600 is invested at two different simple interest rates. The difference between the simple interest amounts earned after 4 years at these two rates is ₹402.80. What is the difference between the two rates of interest (in percentage points)?

Introduction:
This problem checks how simple interest changes when only the rate changes while principal and time remain fixed. Under simple interest, SI is directly proportional to the rate. Therefore, the difference in interest earned equals the principal-time factor multiplied by the difference in rates. We use SI difference to solve reinforcing the idea of linearity in simple interest.

Given Data / Assumptions:

• Principal P = ₹2,600
• Time t = 4 years
• Difference in simple interest = ₹402.80
• Let the difference in rates be Δr percentage points
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Compute the interest difference formula: ΔSI = (P * Δr * t) / 100. Rearrange to solve Δr = (ΔSI * 100) / (P * t). Substitute values and compute carefully.

Step-by-Step Solution:
ΔSI = (P * Δr * t) / 100 Δr = (ΔSI * 100) / (P * t) Δr = (402.80 * 100) / (2600 * 4) Δr = 40280 / 10400 Δr = 3.8730769...% Rounded to two decimals: 3.87%

Verification / Alternative check:
If Δr = 3.87%, then ΔSI = (2600 * 3.87 * 4)/100 = (2600 * 15.48)/100 = 402.48 (close due to rounding). Using the exact ratio gives ₹402.80 exactly.

Why Other Options Are Wrong:
2.63% and 1.58% produce smaller interest differences than ₹402.80. 4.02% produces a larger difference. 3.25% is also short of the required value.

Common Pitfalls:
Forgetting to multiply by time, dividing by 100 incorrectly, or treating ₹402.80 as the total interest rather than the difference between two interests.

Final Answer:
The difference between the two rates is 3.87 percentage points.