Rohan borrows a certain sum of money at simple interest. The rate is 3 percent per annum for the first 3 years, 4 percent per annum for the next 5 years, and 6 percent per annum for the following 7 years. If he pays Rs 2059 as total interest, what is the sum he borrowed in rupees?

Introduction / Context:
This question deals with simple interest when the rate of interest changes over different time intervals, but the principal remains the same. Instead of having one uniform rate for the entire period, we must treat each segment with its own rate and then sum the interests. The total interest is given, and from that we must determine the original sum borrowed by Rohan.

Given Data / Assumptions:
- Rate for the first 3 years: 3 percent per annum.
- Rate for the next 5 years: 4 percent per annum.
- Rate for the following 7 years: 6 percent per annum.
- Total interest paid over all 3 periods together is Rs 2059.
- The principal P is constant during the entire time and must be found.

Concept / Approach:
Under simple interest with varying rates, we add the interest from each period separately. For a period with principal P, rate R, and time T, the interest is:
SI = (P * R * T) / 100We compute the interest for each rate period as a multiple of P, then sum these to get the total interest. This yields one linear equation in P that we can solve easily.

Step-by-Step Solution:
Let P be the principal that Rohan borrowed.First 3 years at 3 %: SI1 = (P * 3 * 3) / 100 = (9P) / 100.Next 5 years at 4 %: SI2 = (P * 4 * 5) / 100 = (20P) / 100.Next 7 years at 6 %: SI3 = (P * 6 * 7) / 100 = (42P) / 100.Total interest SI_total = SI1 + SI2 + SI3.SI_total = (9P + 20P + 42P) / 100 = (71P) / 100.Given that the total interest is Rs 2059, so (71P) / 100 = 2059.Multiply both sides by 100: 71P = 2059 * 100.2059 * 100 = 205900.So, P = 205900 / 71.Compute P: P = 2900.Therefore, Rohan borrowed Rs 2900.

Verification / Alternative check:
We can verify by recomputing the interest with P = 2900. First 3 years: (2900 * 3 * 3) / 100 = (2900 * 9) / 100 = 261. Next 5 years: (2900 * 4 * 5) / 100 = (2900 * 20) / 100 = 580. Next 7 years: (2900 * 6 * 7) / 100 = (2900 * 42) / 100 = 1218. Adding them: 261 + 580 + 1218 = 2059, which matches the given total interest, confirming that P = 2900 is correct.

Why Other Options Are Wrong:
If P were Rs 2400 or Rs 2500, the total interest calculated by the same method would be significantly less than Rs 2059. A principal of Rs 3100 would produce more interest than stated. Rs 2700 would also not match the given total interest. Only a principal of Rs 2900 makes the three period interests add up exactly to Rs 2059.

Common Pitfalls:
Some learners mistakenly use the average of the rates or average of the total years instead of handling each segment separately. Others may forget to convert percentages correctly or may mix up simple and compound interest. The correct approach is always to compute the simple interest for each distinct rate period and then sum them. Carefully treating the 3, 5, and 7 year segments ensures accurate results.

Final Answer:
The sum borrowed by Rohan is Rs 2900.