The compound interest on a certain sum for 2 years at 10% per annum is Rs. 1155. What is the simple interest on the same sum for double the time (4 years) at half the rate (5% per annum)?

Introduction / Context:
This question links compound interest information to a simple interest calculation on the same principal. You must first deduce the principal using the compound interest data, and then use that principal with different time and rate in the simple interest formula. It is a good example of multi-step interest reasoning often seen in aptitude tests.

Given Data / Assumptions:

• Compound interest CI for 2 years at 10% per annum = Rs. 1155
• Rate for CI r1 = 10% per annum
• Time for CI T1 = 2 years
• Same principal P in both cases
• Required: simple interest SI for 4 years at 5% per annum (double time, half rate)

Concept / Approach:
For compound interest with annual compounding:
A = P * (1 + r1 / 100)^2CI = A - PFrom CI we can find P. Once P is known, we use simple interest formula for the second part:
SI = P * r2 * T2 / 100where r2 = 5% and T2 = 4 years.

Step-by-Step Solution:
Step 1: Express CI in terms of P.A = P * (1.10)^2 = P * 1.21CI = A - P = P * 1.21 - P = P * 0.21Step 2: Use given CI to find P.P * 0.21 = 1155P = 1155 / 0.21 = 5500Step 3: Use simple interest formula for double time and half rate.r2 = 5%, T2 = 4 yearsSI = P * r2 * T2 / 100SI = 5500 * 5 * 4 / 100 = 5500 * 20 / 100 = 5500 * 0.2 = Rs. 1100

Verification / Alternative check:
We may quickly re-check the CI step. If principal is Rs. 5500, amount after 2 years at 10% CI is 5500 * 1.21 = 6655, so compound interest is 6655 - 5500 = 1155, matching the given value. This confirms that P = 5500 is correct and thus our simple interest calculation is reliable.

Why Other Options Are Wrong:
Rs. 5500: This is the principal, not the simple interest.Rs. 1400 and Rs. 4120: These arise from misusing the rate, time, or compound interest formula.Rs. 1200: A rough guess that is close to but not equal to the correct simple interest.

Common Pitfalls:
Students sometimes treat the given CI as if it were simple interest and directly apply proportion, which fails here. Another common mistake is to miscompute 10% compound interest for 2 years and obtain the wrong principal. Keeping formulas clear and solving stepwise avoids these errors.

Final Answer:
The simple interest on the same sum for 4 years at 5% per annum is Rs. 1100.