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 over this entire period, what is the sum he originally borrowed in rupees?

Introduction / Context:
This question involves simple interest with different rates applied over consecutive time intervals on the same principal. Rohan borrows a sum at 3 percent for the first 3 years, 4 percent for the next 5 years, and 6 percent for the next 7 years. The total interest is given, and we must find the original principal. Problems like this test your ability to handle piecewise interest rates and to sum the contributions from each time segment correctly under simple interest.

Given Data / Assumptions:

• Principal P is unknown.
• Rate r₁ = 3 percent per annum for the first 3 years.
• Rate r₂ = 4 percent per annum for the next 5 years.
• Rate r₃ = 6 percent per annum for the following 7 years.
• Total interest paid over all these years is Rs. 2059.
• Interest is simple interest, calculated separately on the same principal for each segment.

Concept / Approach:
Under simple interest, for each segment the interest is:
SI = (Principal * Rate * Time) / 100.
Since the principal P is constant, we can calculate the interest expression for each sub-period in terms of P and then add all three. The sum of these interests equals Rs. 2059. This yields a single linear equation in P. Solving that equation gives the principal borrowed by Rohan.

Step-by-Step Solution:
Step 1: Let the principal be P rupees. Step 2: Interest for the first 3 years at 3 percent: SI₁ = (P * 3 * 3) / 100 = (9P) / 100. Step 3: Interest for the next 5 years at 4 percent: SI₂ = (P * 4 * 5) / 100 = (20P) / 100. Step 4: Interest for the next 7 years at 6 percent: SI₃ = (P * 6 * 7) / 100 = (42P) / 100. Step 5: Total simple interest = SI₁ + SI₂ + SI₃ = (9P/100) + (20P/100) + (42P/100) = (71P/100). Step 6: We are told that this total interest equals Rs. 2059, so (71P / 100) = 2059. Step 7: Rearrange to get P = (2059 * 100) / 71. Step 8: Compute 2059 / 71 = 29, so P = 29 * 100 = 2900. Step 9: Therefore, Rohan originally borrowed Rs. 2900.

Verification / Alternative check:
We can verify by computing the interest in each segment with P = 2900. First 3 years at 3 percent: SI₁ = 2900 * 3 * 3 / 100 = 261. Next 5 years at 4 percent: SI₂ = 2900 * 4 * 5 / 100 = 580. Next 7 years at 6 percent: SI₃ = 2900 * 6 * 7 / 100 = 1218. Summing them: 261 + 580 + 1218 = 2059, which matches the total interest given. This confirms the principal P = 2900 is correct.

Why Other Options Are Wrong:
At Rs. 2400, 2500, 2700, or 3100, the total interest calculated using the same rates and times would not equal Rs. 2059. For example, at P = 2500, the total interest becomes (71 * 2500) / 100 = 1775, which is much lower than 2059. At P = 3100, the total interest would be (71 * 3100) / 100 = 2201, higher than 2059. Only P = 2900 gives the correct total interest of 2059.

Common Pitfalls:
Students sometimes incorrectly apply each new rate to the accumulated amount instead of the principal, effectively mixing compound interest ideas into a simple interest problem. Another pitfall is miscalculating the combined coefficient 9 + 20 + 42 = 71, leading to an incorrect total interest expression. Others try to average the rates over the total time period without weighting for years, which is not needed in this direct algebraic approach. Carefully summing the segment-wise simple interest expressions avoids these mistakes.

Final Answer:
The sum borrowed by Rohan, given the varying simple interest rates over 15 years and a total interest of Rs. 2059, is Rs. 2900.