Simple Interest — Tiered rates; interest exceeds principal: Pratap borrows at simple interest: 12% p.a. for 3 years, 16% p.a. for the next 5 years, and 20% p.a. thereafter. Over 11 years, the total SI exceeds the principal by Rs 6080. Find the principal.

Introduction / Context:When SI over a period is stated to exceed the principal by a known amount, we form an equation where (total SI factor) * P = P + excess, and solve for P after computing the piecewise factor.

Given Data / Assumptions:

• Years 1–3: 12% ⇒ 0.12 * 3 = 0.36
• Years 4–8: 16% ⇒ 0.16 * 5 = 0.80
• Years 9–11: 20% ⇒ 0.20 * 3 = 0.60
• Total SI = P + Rs 6080 (i.e., exceeds principal by 6080)

Concept / Approach:Compute SI factor f = 0.36 + 0.80 + 0.60 = 1.76. Set f * P = P + 6080 ⇒ (1.76 − 1) P = 6080 ⇒ 0.76 P = 6080 ⇒ P = 8000.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other principals do not satisfy (1.76 − 1) P = 6080.

Common Pitfalls:

• Interpreting “exceeds by” as “equals”.

Final Answer:Rs 8000.