A sum of money is invested for 3 years at a certain rate of simple interest. If it had instead been invested at a rate that is 4% higher per annum, the total simple interest earned in 3 years would have been Rs. 600 more. Find the original sum invested.

Introduction / Context:
This question deals with how a change in the rate of simple interest affects the total interest earned over a fixed time period. Instead of giving the rate directly, the question describes what would happen if the rate were increased by 4 percent per annum and states how much extra interest would be obtained. From this information we must deduce the initial principal. Such problems are common in aptitude exams and require a clear understanding of how interest varies with rate under simple interest.

Given Data / Assumptions:
Initial rate of interest is r percent per annum (unknown).
Time period is 3 years in both cases.
Principal amount is P rupees (unknown).
New rate of interest would be r + 4 percent per annum.
The difference in total interest over 3 years between the two rates is Rs. 600.
Interest is calculated as simple interest in both scenarios.

Concept / Approach:
For simple interest, I = P * r * t / 100. If the rate increases by 4 percent, the new interest is P * (r + 4) * t / 100. The extra interest due to the higher rate is the difference between these two amounts. Since P and t are the same in both cases, the difference depends only on the 4 percent increase in rate. This leads to a neat equation where the extra interest equals P * 4 * t / 100. Using the given extra interest of 600 rupees, we can solve for P directly.

Step-by-Step Solution:
Let the original principal be P rupees and the original rate be r percent per annum.Original interest for 3 years is I1 = P * r * 3 / 100.With the rate increased by 4 percent, the interest becomes I2 = P * (r + 4) * 3 / 100.The extra interest is I2 - I1 = 600 rupees.Compute I2 - I1 = P * (r + 4) * 3 / 100 - P * r * 3 / 100.Factor out P * 3 / 100 to get I2 - I1 = P * 3 / 100 * [(r + 4) - r] = P * 3 / 100 * 4.So extra interest equals P * 12 / 100 = 0.12P.Set this equal to 600: 0.12P = 600.Solve for P to get P = 600 / 0.12 = 5000.Therefore the original sum invested is Rs. 5000.

Verification / Alternative check:
With P = 5000, the extra interest for a 4 percent increase in rate over 3 years is P * 4 * 3 / 100 = 5000 * 12 / 100 = 600 rupees. This matches the given increase in interest. Since the relationship depends only on the product of principal, change in rate, and time, our result is fully consistent, and no other principal will satisfy the given condition.

Why Other Options Are Wrong:
For P = 4000, extra interest would be 4000 * 12 / 100 = 480 rupees, which is less than 600 rupees.
For P = 4950, extra interest becomes 4950 * 12 / 100 = 594 rupees, not equal to 600 rupees.
For P = 5150, extra interest is 618 rupees, again not matching 600 rupees.
For P = 6000, extra interest is 720 rupees, which is too high. Thus these options do not satisfy the given condition.

Common Pitfalls:
One common mistake is to think that the extra interest of 600 rupees comes only from a single year rather than from the full 3 year period. Another error is to treat the 4 percent as 0.4 rather than 4 when substituting into the formula, or to forget dividing by 100. Some learners also attempt to find the original rate, although it is not needed to answer the question. Focusing directly on the change in rate and using the difference formula helps simplify the problem.

Final Answer:
The original sum invested under simple interest is Rs. 5000.