Simple Interest – Find principal from difference due to rate increase: A sum is invested for 2 years at simple interest. If the rate is increased by 3% per annum, the total interest earned becomes ₹ 300 more. Find the principal.

Introduction / Context:
When only the rate changes in simple interest, the change in interest is directly proportional to the principal and time. This allows us to solve for principal without knowing the original rate.

Given Data / Assumptions:

• Time t = 2 years
• Increase in rate Δr = 3% per annum
• Increase in total interest ΔI = ₹ 300
• Simple interest difference formula applies: ΔI = P * Δr * t / 100

Concept / Approach:
Rearrange the difference formula to P = (ΔI * 100) / (Δr * t). This avoids computing the absolute interests at both rates.

Step-by-Step Solution:
P = (300 * 100) / (3 * 2)P = 30,000 / 6 = 5,000

Verification / Alternative check:
At Δr = 3% for 2 years, extra interest on ₹ 5,000 is 5,000 * 3 * 2 / 100 = ₹ 300, which matches the given difference.

Why Other Options Are Wrong:
₹ 6,000, ₹ 7,000, ₹ 4,000, and ₹ 8,000 yield differences of ₹ 360, ₹ 420, ₹ 240, and ₹ 480 respectively under the same Δr and t, not ₹ 300.

Common Pitfalls:
Forgetting to divide by 100, or misreading percentage points as decimal fractions, can cause scaling errors. Keep Δr in percent in the standard SI formula.

Final Answer:
₹ 5,000