In a compound interest and simple interest comparison problem, the compound interest on a certain sum of money at 20% per annum for 2 years is Rs. 5995. On the same principal amount, what will be the simple interest at 8% per annum for 6 years?

Introduction / Context:
This question connects compound interest (C.I.) and simple interest (S.I.) on the same principal. You are given the compound interest at a higher rate and shorter period, and you must find the simple interest at a lower rate and longer period. It tests your understanding of how to back-calculate the principal from compound interest and then use the simple interest formula.

Given Data / Assumptions:
- Compound interest for 2 years at 20% per annum is Rs. 5995.
- Let the principal be P rupees.
- Rate for C.I. = 20% per annum, time = 2 years, compounded annually.
- We then invest the same principal at simple interest at 8% per annum for 6 years.
- We must find the simple interest for this second case.

Concept / Approach:
First, use the compound interest formula to find the principal:
Amount with C.I. = P * (1 + 20/100)^2 = P * (1.2)^2 = 1.44P.
Compound interest = 1.44P - P = 0.44P.
This C.I. is given as Rs. 5995, so we can solve for P. Once P is known, apply the simple interest formula S.I. = P * R * T / 100 for 8% per annum and 6 years.

Step-by-Step Solution:
Step 1: From the compound interest data, 0.44P = 5995.Step 2: Solve for P: P = 5995 / 0.44 = 13625.Step 3: For simple interest, rate R = 8% per annum and time T = 6 years.Step 4: Use S.I. formula: S.I. = P * R * T / 100.Step 5: S.I. = 13625 * 8 * 6 / 100.Step 6: Compute: 13625 * 8 = 109000; 109000 * 6 = 654000; 654000 / 100 = 6540.Step 7: Therefore, the required simple interest is Rs. 6540.

Verification / Alternative check:
You can quickly check the principal by multiplying 13625 by 0.44: 10% of 13625 is 1362.5, so 40% is 5450; 4% is 545; total 44% is 5450 + 545 = 5995, which matches the given C.I. Hence the principal is correct, and so is the simple interest of Rs. 6540.

Why Other Options Are Wrong:
Rs. 5989 and Rs. 6789 are close in magnitude but result from rounding errors or incorrect principal calculation. Rs. 7844 and Rs. 7200 come from using the wrong interest rate or time period in the simple interest formula. Only Rs. 6540 correctly uses the principal 13625 with 8% for 6 years.

Common Pitfalls:
Many learners mistakenly treat the given compound interest as simple interest and directly apply S.I. formulas, which leads to an incorrect principal. Others confuse amount and interest, using 1.44P instead of 0.44P. Always remember that compound interest = amount minus principal, and be careful when switching between C.I. and S.I. formulas.

Final Answer:
The simple interest on the same sum at 8% per annum for 6 years is Rs. 6540.