A sum of money is invested for 3 years at a certain rate of simple interest. If instead it had been invested at a rate that is 4% higher per annum, the total simple interest earned in the same 3 years would have been Rs 600 more than before. Using this information about the change in interest, find the original sum invested.

Introduction / Context: This problem tests the ability to work with changes in interest rate under simple interest. When the interest rate is increased by a fixed percentage, the extra interest earned over a given time can be related directly to the principal. Instead of giving the actual rate, the question provides the increase in rate (4% per annum) and the resulting increase in interest (Rs 600 in 3 years). The task is to use the simple interest formula to relate these quantities and solve for the principal or original sum invested.

Given Data / Assumptions:

• Time period T = 3 years.
• Original rate of interest = R% per annum (unknown).
• New rate of interest = (R + 4)% per annum.
• Increase in total simple interest over 3 years when rate increases by 4% = Rs 600.
• Original principal or sum invested = P rupees (unknown).
• Interest is calculated using simple interest for both scenarios.

Concept / Approach: Simple interest is given by: SI = (P * R * T) / 100 When the rate increases from R to R + 4, the difference in interest for the same principal and time is due only to the change in rate. The extra interest is: Extra SI = (P * (R + 4) * T) / 100 − (P * R * T) / 100 This simplifies neatly because the R terms cancel out, leaving an expression in terms of P, T, and the rate change 4. By equating that extra interest to Rs 600, we can solve for P directly.

Step-by-Step Solution: Let the original principal be P rupees. Original simple interest for 3 years at R% = (P * R * 3) / 100. New simple interest for 3 years at (R + 4)% = (P * (R + 4) * 3) / 100. Increase in interest = New SI − Old SI. Increase in interest = (P * (R + 4) * 3) / 100 − (P * R * 3) / 100. Factor out P * 3 / 100: Increase = (P * 3 / 100) * ((R + 4) − R) = (P * 3 / 100) * 4. So increase in interest = (P * 12) / 100 = 0.12P. Given that this increase equals Rs 600, we have 0.12P = 600. Therefore, P = 600 / 0.12 = 5000. Thus, the original sum invested is Rs 5000.

Verification / Alternative check: To verify, choose any convenient original rate, for example R = 10% per annum. At 10% for 3 years on Rs 5000, SI = (5000 * 10 * 3) / 100 = 1500. At the increased rate of 14%, SI = (5000 * 14 * 3) / 100 = 2100. Difference in interest = 2100 − 1500 = Rs 600, which matches the question. The choice of R is arbitrary because the difference depends only on the 4% increase, confirming that P = Rs 5000 is correct.

Why Other Options Are Wrong: If P were Rs 4000, then extra interest at 4% for 3 years would be (4000 * 4 * 3) / 100 = Rs 480, not 600. If P were Rs 4950, the extra interest would be (4950 * 4 * 3) / 100 = Rs 594, slightly less than 600. If P were Rs 5150, the extra interest would be Rs 618, larger than 600. If P were Rs 6000, the extra interest would be Rs 720. Therefore these options do not satisfy the condition that the increase in interest is Rs 600.

Common Pitfalls: A common mistake is to attempt to find the original rate R first, even though it is not needed. Another error is to use 4 as the total interest rather than as the change in rate. Some students also forget to multiply by time when computing the extra interest, using P * 4 / 100 instead of P * 4 * 3 / 100. Focusing on the structure of the formula and carefully substituting the change in rate over the full time period avoids these errors.

Final Answer: The original principal or sum of money invested is Rs 5000.