The total simple interest earned on a certain sum of money increases by Rs 600 when the rate of interest is increased by 2% per annum. If the investment is made for 5 years at simple interest, what is the principal (sum of money) originally invested?

Introduction / Context:
This question is about how changes in the rate of simple interest affect the total interest over a fixed time. When the rate increases by a certain percentage, the interest increases proportionally to the principal and time. The problem tells you the increase in interest due to an increase in rate, and asks you to find the principal, which is a direct application of the simple interest formula.

Given Data / Assumptions:

Principal P is unknown.
Time T = 5 years.
Rate increases by 2% per annum (that is, from r% to (r + 2)% per annum).
Increase in total simple interest over 5 years = Rs 600.
Simple interest formula: SI = (P * R * T) / 100.

Concept / Approach:
When the rate increases from r% to (r + 2)%, the change in interest over the same principal P and time T is determined only by the additional 2%. The extra simple interest can therefore be computed using just the increment in rate, the principal, and the time. We treat the increase as simple interest at 2% per annum for 5 years on the same principal, and equate it to Rs 600, then solve for P.

Step-by-Step Solution:
Step 1: Let original principal be P. Step 2: Additional rate of interest = 2% per annum. Step 3: Time T = 5 years. Step 4: Extra simple interest caused by the extra 2% rate is given as Rs 600. Step 5: Using SI = (P * R * T) / 100 for this extra part, we have 600 = (P * 2 * 5) / 100. Step 6: Simplify the right side: (P * 2 * 5) / 100 = (10P) / 100 = P / 10. Step 7: Therefore, P / 10 = 600. Step 8: Multiply both sides by 10 to get P = 600 * 10 = 6000. Step 9: Hence, the principal invested is Rs 6,000.

Verification / Alternative check:
As a quick check, consider the extra interest as if principal is 6000, rate increase is 2%, and time is 5 years. Extra SI = (6000 * 2 * 5) / 100 = (6000 * 10) / 100 = 60000 / 100 = 600, which matches the given increase. This confirms that P = 6000 is consistent.

Why Other Options Are Wrong:
If P were 5550, 7500, 6580, or 7200, the extra interest at 2% for 5 years would be different from Rs 600. For example, with P = 7500, extra SI would be (7500 * 2 * 5) / 100 = 750, not 600. Thus, those options do not satisfy the condition provided.

Common Pitfalls:
Many learners unnecessarily introduce the original rate r into the calculation, which is not required. Others may forget that the increase in rate applies for the entire period of 5 years, not just for one year. Focus on the fact that extra interest is directly due to the extra 2% rate over the full time on the same principal.

Final Answer:
The principal originally invested is Rs 6,000.