CI–SI Comparison — Find rate from 2-year difference and SI total: For a sum, the difference between compound and simple interest for 2 years is ₹ 160. The simple interest for 2 years is ₹ 2880. Find the annual rate (percent per annum).

Introduction / Context:Two years at the same annual rate produces neat identities: SI(2y) = 2 P r and CI − SI = P r^2, where r is the annual rate in decimal and P is the principal. Having both the 2-year SI and the 2-year difference allows elimination of P to solve directly for r, then convert it to a percent value.

Given Data / Assumptions:

• SI over 2 years = ₹ 2880 ⇒ 2 P r = 2880
• CI − SI over 2 years = ₹ 160 ⇒ P r^2 = 160
• r is an annual rate (decimal), P > 0

Concept / Approach:Divide the two equations to eliminate P: (P r^2)/(2 P r) = r/2 = 160/2880. This quickly yields r. Finally, express r as a mixed fraction percentage for clarity.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 9%, 10%, 12 1/2%, 55/9% do not satisfy both equations simultaneously; only 11 1/9% works.

Common Pitfalls:

• Treating r as “11.1” instead of 0.111…; always convert properly between decimal and percent.

Final Answer:11 1/9% per annum.