Divide Rs 8000 into two parts so that simple interest on the 1st part for 2…

Concept: Simple Interest (SI) on a principal P for T years at rate R% p.a. is SI = (P × R × T) / 100. Compound Interest (CI) on a principal P for T years at rate R% p.a., compounded annually, is CI = P × [(1 + R/100)T − 1]. When a sum is split into two parts linked by an SI/CI condition, set up this equation and solve for the parts.

Applying to this question:

1. Let the 1st part be Rs x, so the 2nd part is Rs (8000 − x).

2. SI on the 1st part for 2 years at 6.5% p.a.: SI = (x × 6.5 × 2) / 100 = 0.13x.

3. CI on the 2nd part for 2 years at 5% p.a.: CI = (8000 − x) × [(1.05)2 − 1] = (8000 − x) × 0.1025.

4. Since SI = CI: 0.13x = 0.1025(8000 − x).

5. Expand the right side: 0.13x = 820 − 0.1025x.

6. Combine like terms: 0.13x + 0.1025x = 820, so 0.2325x = 820.

7. Solve for x: x = 820 / 0.2325 ≈ 3526.88.

8. So the 1st part ≈ Rs 3,526.88 and the 2nd part = 8000 − 3526.88 ≈ Rs 4,473.12.

Cross-check: This computed split (≈ Rs 3,526.88 and ≈ Rs 4,473.12) does not match any of the numeric splits offered — Rs. 2,000/Rs. 6,000; Rs. 2,500/Rs. 5,500; or Rs. 3,000/Rs. 5,000 — confirming that the correct choice is ‘None of these’.