The difference between the simple interest received from two different sources…

Concept: Simple Interest is SI = (P × T × R) / 100, where P is the principal, T is the time in years and R is the annual rate. When the same principal is invested for the same time at two different rates R₁ and R₂, the difference between the two simple interests is directly proportional to the difference between the rates: SI₁ − SI₂ = (P × T × (R₁ − R₂)) / 100.

Application

1. Let the two rates of interest be R₁ and R₂, so the required difference is R₁ − R₂.

2. Given: Principal P = ₹2000, Time T = 4 years, and the difference between the two simple interests = ₹80.

3. Substitute into SI₁ − SI₂ = (P × T × (R₁ − R₂)) / 100: 80 = (2000 × 4 × (R₁ − R₂)) / 100.

4. Simplify the right-hand side: 80 = 80 × (R₁ − R₂).

5. Divide both sides by 80: R₁ − R₂ = 1.

Cross-check: With a rate difference of 1%, the interest difference works out to (2000 × 4 × 1) / 100 = ₹80, which matches the amount given in the question.

So the difference between the two rates of interest is 1%.