Compound vs Simple Interest – Convert CI over 2 years at 10% to equivalent SI: The compound interest on a certain principal for 2 years at 10% per annum is ₹ 420. What is the simple interest on the same principal at the same rate for the same time?

Introduction / Context:
This problem asks you to translate a given compound interest (CI) result into the corresponding simple interest (SI) for the same principal, rate, and time. Once you recover the principal from the CI information, SI becomes a straightforward product of P, r, and t.

Given Data / Assumptions:

• CI over 2 years at r = 10% per annum is ₹ 420
• Compounding is annual
• We need SI for the same P, r, and t

Concept / Approach:
For annual compounding over 2 years, amount factor is (1 + 0.10)^2 = 1.21. Let principal be P. Then A − P = CI = 0.21P = 420, giving P = 2,000. Under simple interest, I_SI = P * r * t / 100 = 2,000 * 10 * 2 / 100 = 400.

Step-by-Step Solution:
CI relation: 0.21P = 420 ⇒ P = 420 / 0.21 = 2,000SI for same terms: I_SI = 2,000 * 10 * 2 / 100 = 400

Verification / Alternative check:
Direct check of CI amount: A = 2,000 * 1.21 = 2,420, so CI = 420. SI for 2 years is 20% of 2,000 = 400, as computed.

Why Other Options Are Wrong:
₹ 350, ₹ 375, ₹ 380, and ₹ 360 are not equal to 20% of ₹ 2,000 for 2 years and therefore do not match the same P, r, t under SI.

Common Pitfalls:
Trying to convert CI to SI without first recovering principal can lead to confusion. Always infer P from the CI setup, then compute SI directly.

Final Answer:
₹ 400