Simple Interest – Find principal from ₹ 24 extra due to 1% higher rate over 2 years: A sum is invested for 2 years at simple interest. If raising the rate by 1% per annum increases the total interest by ₹ 24, find the principal.

Introduction / Context:This is a direct application of the simple-interest difference formula: the extra interest generated by a change in rate over a fixed time is proportional to the principal. We can solve for the principal without knowing the original rate.

Given Data / Assumptions:

• Time t = 2 years
• Rate increase Δr = 1% per annum
• Extra interest ΔI = ₹ 24

Concept / Approach:Use ΔI = P * Δr * t / 100 ⇒ P = (ΔI * 100) / (Δr * t). Substitute the given values directly.

Step-by-Step Solution:P = (24 * 100) / (1 * 2) = 2,400 / 2 = 1,200

Verification / Alternative check:At Δr = 1% for 2 years, extra interest on ₹ 1,200 is 1,200 * 1 * 2 / 100 = ₹ 24, matching the statement.

Why Other Options Are Wrong:₹ 600, ₹ 800, ₹ 480, and ₹ 1,000 produce extra interests of ₹ 12, ₹ 16, ₹ 9.6, and ₹ 20 respectively under the same Δr and t, not ₹ 24.

Common Pitfalls:Confusing “1% higher” with multiplying the rate by 1.01, or forgetting that percent must be divided by 100 in SI computations.

Final Answer:₹ 1,200