Simple Interest — Borrow low, lend high arbitrage: Prabhat borrows at 8% p.a. SI and lends the same sum to Ashish at 12% p.a. SI. If his profit in 2 years is Rs 320, how much did he borrow?

Introduction / Context:Arbitrage under SI arises from lending at a higher rate than the borrowing rate. The net gain equals principal times the rate spread times time.

Given Data / Assumptions:

• Borrowing rate = 8% p.a.
• Lending rate = 12% p.a.
• Time = 2 years
• Profit = Rs 320

Concept / Approach:Profit = P * (rate spread) * t = P * (0.12 − 0.08) * 2 = 0.08 * P. Solve 0.08 * P = 320 for P.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 2000, 3000, 5000, 6000 do not yield a spread-based profit of 320 over 2 years.

Common Pitfalls:

• Using 12% − 8% = 2% instead of 4%; the spread is 4% per annum.

Final Answer:Rs 4000.