Simple Interest — Piecewise annual rates over 9 years: A sum earns SI at 4% p.a. for the first 2 years, 6% p.a. for the next 4 years, and 8% p.a. for the period beyond 6 years. If total SI in 9 years is Rs 1120, find the principal.

Introduction / Context:With simple interest, different flat rates over disjoint time blocks add linearly. Summing each block’s contribution gives the overall SI factor times the principal.

Given Data / Assumptions:

• Years 1–2: 4% p.a. ⇒ 0.04 * 2
• Years 3–6: 6% p.a. ⇒ 0.06 * 4
• Years 7–9: 8% p.a. ⇒ 0.08 * 3
• Total SI = Rs 1120 over 9 years

Concept / Approach:Total SI factor = 0.04*2 + 0.06*4 + 0.08*3. Multiply this factor by P to equal Rs 1120, then solve for P.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1500, 1800, 2500, 4000 produce total SI unequal to Rs 1120 using the same block factors.

Common Pitfalls:

• Misallocating years across blocks or mixing up rates.

Final Answer:Rs 2000.