Credit sale and real gain: A motor-cycle costs ₹32500. It is sold for ₹35000 on 6-month credit. If money is worth 4% per annum (simple), what is the seller’s actual gain percentage based on the true present value of the credit sale?

Introduction / Context:
When goods are sold on credit, the cash-equivalent present value is lower than the listed credit price. To find the true gain, discount the credit price back to today at the money value (opportunity cost) and compare this present value to the cost price. This avoids overstating profit by ignoring the time value of money.

Given Data / Assumptions:

• Cost price C = ₹32500.
• Credit selling price after 6 months S = ₹35000.
• Money worth r = 4% per annum (simple), time t = 0.5 year.
• Use simple true discount to find present value.

Concept / Approach:
Present value PV = S / (1 + r * t). Real gain = PV − C. Gain% = (Real gain / C) * 100. This compares like with like in today’s rupees.

Step-by-Step Solution:

Verification / Alternative check:
Using simple interest deduction: PV = 35000 − (35000 * 0.04 * 0.5) = 35000 − 700 = ₹34300. Then gain% = (34300 − 32500)/32500 = 1800/32500 ≈ 5.54%, consistent with ≈ 5.5%.

Why Other Options Are Wrong:
The higher mixed-fraction percentages (e.g., 7 5/13%, 8 1/7%, 8 2/5%, 7 9/13%) ignore the required discounting and overstate profit.

Common Pitfalls:
Computing gain on the nominal ₹35000 without discounting; mixing up base (cost versus present value) when expressing the percentage.

Final Answer:
5.5%