Simple Interest — Neeta borrows at tiered simple interest: 6% p.a. for the first 3 years, 9% p.a. for the next 5 years, and 13% p.a. for the period beyond 8 years. If the total interest paid in 11 years is ₹ 8160, find the principal borrowed.

Introduction / Context:
When the simple interest rate changes across disjoint periods, total interest equals principal times the sum of periodwise rates * years. The principal can be factored out.

Given Data / Assumptions:

• Years 1–3: 6% p.a.
• Years 4–8: 9% p.a.
• Years 9–11: 13% p.a.
• Total SI over 11 years = ₹ 8160.

Concept / Approach:
Let P be principal. Then SI_total = P*(0.06*3 + 0.09*5 + 0.13*3) = P*(0.18 + 0.45 + 0.39) = P*1.02.

Step-by-Step Solution:
P * 1.02 = 8160 ⇒ P = 8160 / 1.02 = ₹ 8,000.

Verification / Alternative check:
Annualized interest: 6%*3=18%, 9%*5=45%, 13%*3=39%; total 102% of P = ₹ 8160 ⇒ P = 8000.

Why Other Options Are Wrong:
₹ 12,000, ₹ 10,000, ₹ 9,000 do not satisfy the 1.02 multiplier.

Common Pitfalls:
Confusing percentage points with percent of P; under SI, add (rate * years) linearly.

Final Answer:
₹ 8,000