CI vs SI — Use 2-year difference to infer rate, then extend to 3 years: For a sum, CI for 2 years is ₹ 832 while SI for 2 years is ₹ 800. What is the difference (CI − SI) for 3 years at the same annual rate?

Introduction / Context:Differences between CI and SI have closed-form expressions: for 2 years, CI − SI = P r^2; for 3 years, CI − SI = P r^2 (3 + r), where r is the annual rate in decimal and P the principal. Given the 2-year CI and SI, we can find r (or P and r) and compute the 3-year difference directly.

Given Data / Assumptions:

• CI(2y) = ₹ 832; SI(2y) = ₹ 800
• Thus, CI − SI (2y) = ₹ 32
• Annual rate r same for all years

Concept / Approach:From SI(2y) = 2 P r = 800 ⇒ P r = 400. From the difference identity, P r^2 = 32. Divide to get r = (P r^2)/(P r) = 32/400 = 0.08 = 8%. Then apply the 3-year formula for the difference: P r^2 (3 + r). Compute P via P = (P r)/r = 400/0.08 = 5000.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 48, ₹ 66.56, and other figures do not match P r^2 (3 + r) at r = 8% and P = 5000.

Common Pitfalls:

• Using 2-year identity (P r^2) again for 3 years; the 3-year expression includes the (3 + r) factor.

Final Answer:Rs. 98.56.