Simple Interest — Mixed rates over 8 years: Rate is 5% p.a. for the first 2 years, 8% p.a. for the next 3 years, and 10% p.a. thereafter. If the total simple interest in 8 years is Rs 1280, find the principal.

Introduction / Context:
Piecewise constant rates under simple interest sum to an overall factor multiplying the principal. Carefully allocate the correct years to each rate block and add the contributions.

Given Data / Assumptions:

• Years 1–2: 5% ⇒ 0.05 * 2
• Years 3–5: 8% ⇒ 0.08 * 3
• Years 6–8: 10% ⇒ 0.10 * 3
• Total SI over 8 years = Rs 1280

Concept / Approach:
Total factor = 0.05*2 + 0.08*3 + 0.10*3. Multiply by P to equal 1280; solve for P.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other values of P do not satisfy 0.64 * P = 1280.

Common Pitfalls:

• An arithmetic slip on the first block (ensure 0.05 * 2 * 2000 = 200).

Final Answer:
Rs 2000.