Rising yearly rates under simple interest — find principal: A loan runs for 5 years with simple interest rates of 7% in year 1 and increasing by 0.5% each subsequent year. If the total interest paid over the 5 years is ₹ 3690, how much was originally borrowed?

Introduction / Context:
Under simple interest with piecewise-constant annual rates, the total interest equals principal times the sum of yearly rates (expressed in percent) divided by 100.

Given Data / Assumptions:

• Yearly rates: 7.0%, 7.5%, 8.0%, 8.5%, 9.0%
• Sum of yearly rates over 5 years = 40.0%
• Total SI = ₹ 3690

Concept / Approach:
Total SI = P * (sum_of_rates) / 100. Hence P = Total_SI * 100 / (sum_of_rates).

Step-by-Step Solution:
Sum of rates = 7 + 7.5 + 8 + 8.5 + 9 = 40%3690 = P * 40 / 100 → P = 3690 / 0.40 = ₹ 9225

Verification / Alternative check:
Compute interest year-wise with P = 9225 and sum; it totals ₹ 3690 (by construction).

Why Other Options Are Wrong:
₹ 9250, ₹ 9440, or ₹ 9360 correspond to rounding or arithmetic deviations; the exact computation yields ₹ 9225.

Common Pitfalls:
Assuming compounding or averaging the rates incorrectly rather than summing for SI. Also, forgetting to divide by 100.

Final Answer:
₹ 9225