Simple interest on a sum for 3 years at 8% p.a. equals half the compound interest on Rs. 4,000 for 2 years at 10% p.a. Find the sum placed at simple interest.

Problem restatement
Compute CI on Rs. 4,000 for 2 years at 10%, halve it, and set equal to SI on unknown principal at 8% for 3 years.

Given data

• CI (4,000; 10%; 2 years) = 4,000[(1.10)² − 1] = 4,000(0.21) = 840
• Half of that = 420
• SI = P × 0.08 × 3 = 0.24P

Step-by-step calculation
0.24P = 420P = 420 ÷ 0.24 = Rs. 1,750

Verification/Alternative
Check: SI = 1,750 × 0.24 = 420, which is indeed half of 840.

Common pitfalls
Using 10% of 4,000 twice without compounding (that would be SI, not CI).

Final Answer
Rs. 1,750