The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 1,155. What will be the simple interest on the same sum at half this rate (that is, 5% per annum) for double the time (that is, 4 years)?

Introduction:
In this problem we are given a compound interest figure and asked to determine a simple interest figure for a different rate and time, but for the same principal. This links both types of interest and checks whether you can extract the principal from the compound interest data and then apply the simple interest formula correctly.

Given Data / Assumptions:
Compound interest CI = Rs. 1,155. Rate for CI r₁ = 10% per annum. Time for CI t₁ = 2 years, compounded annually. For SI: rate r₂ = 5% per annum (half of 10%). Time for SI t₂ = 4 years (double of 2 years).

Concept / Approach:
First, use the compound interest formula for 2 years: A = P * (1 + 10/100)^2 = P * 1.21. Then CI = A − P = 0.21P. Since CI is given, we can solve for P. After getting P, we apply the simple interest formula: SI = P * r₂ * t₂ / 100.

Step-by-Step Solution:
Step 1: Get principal from CI. CI = 0.21P = 1,155. P = 1155 / 0.21. P = 115500 / 21 = Rs. 5,500. Step 2: Apply SI at 5% for 4 years. SI = P * r₂ * t₂ / 100. SI = 5500 * 5 * 4 / 100. SI = 5500 * 20 / 100 = 5500 / 5 = Rs. 1,100.

Verification / Alternative check:
We can verify the principal by recomputing the compound interest: A = 5500 * 1.21 = Rs. 6,655. CI = A − P = 6655 − 5500 = Rs. 1,155, which matches the given CI. This confirms that P is correct and thus the simple interest calculation is reliable.

Why Other Options Are Wrong:
Rs. 5,500 and Rs. 4,120 correspond more to principal or amount figures rather than the interest over 4 years at 5%. Rs. 1,400 and Rs. 950 arise from misapplication of time or rate, such as forgetting that the rate is halved and the time is doubled, or making arithmetic mistakes in multiplying 5500 * 20 / 100.

Common Pitfalls:
One common error is to treat Rs. 1,155 as simple interest and use SI formula directly to find P, which would give a wrong value. Another mistake is to forget to double the time while halving the rate in the second part. Clear separation of the two stages avoids confusion.

Final Answer:
The simple interest for 4 years at 5% per annum on the same sum is Rs. 1,100.