A man purchases a cow for Rs 3000 in cash and sells it on the same day for Rs 3600, allowing the buyer a credit period of 2 years. If the rate of interest is 10 percent per annum, what is the man's effective gain or loss percentage on this transaction?

Introduction / Context:
This question combines the ideas of cost price, selling price and the time value of money. The seller receives a higher nominal selling price, but only after a period of 2 years. When interest is taken into account, the real or present worth of the selling price may be different. The question asks whether there is a real profit or loss when we discount the future payment back to its present value.

Given Data / Assumptions:
- Cost price of the cow = Rs 3000 paid in cash now.
- Selling price nominally = Rs 3600, but this is to be received after 2 years.
- Rate of interest = 10 percent per annum (simple interest assumed).
- There are no other costs or charges involved.
- We need to compare the present value of the delayed selling price with the immediate cost price to find the effective gain or loss percentage.

Concept / Approach:
The key concept is present value. A payment of Rs 3600 two years later does not have the same value as receiving Rs 3600 today, because money now can earn interest. To compare fairly with the cost price of Rs 3000 paid today, we find the present value of Rs 3600 due after 2 years at 10 percent simple interest. Present value is given by amount divided by (1 + r * t), where r is the rate in decimal and t is the time in years. We then compare this present value with the cost price to determine the gain or loss.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs 3000 paid now. Step 2: Nominal selling price (SP) = Rs 3600, but receivable after 2 years. Step 3: Rate r = 10 percent per annum, time t = 2 years. Step 4: Present value (PV) of Rs 3600 due after 2 years at 10 percent simple interest = 3600 / (1 + r * t). Step 5: Compute denominator: 1 + 0.10 * 2 = 1 + 0.20 = 1.20. Step 6: PV = 3600 / 1.20 = Rs 3000. Step 7: Effective comparison: CP = Rs 3000 now, PV of SP = Rs 3000 now, so there is no real gain or loss.

Verification / Alternative check:
If the man deposits Rs 3000 at 10 percent simple interest for 2 years, it becomes 3000 * (1 + 0.10 * 2) = 3000 * 1.20 = Rs 3600 at the end of 2 years. This is exactly the amount he will receive from the buyer after 2 years. Therefore, from a present value perspective, his situation is the same as if he had simply invested his cost price at the bank at the given interest rate. Hence his effective gain is zero percent.

Why Other Options Are Wrong:
Options 5 percent, 7.5 percent and 10 percent all assume some net gain over the cost price when properly discounted. However, the discounting calculation shows that the present value of Rs 3600 after 2 years is exactly equal to Rs 3000, not higher. Therefore none of these positive gain percentages is correct.

Common Pitfalls:
A common mistake is to look only at the nominal difference between 3600 and 3000 and conclude there is a 20 percent profit. This ignores the time value of money and the fact that the payment is delayed for 2 years. True evaluation must compare values at the same point in time by discounting future amounts back to the present using the given interest rate.

Final Answer:
The man makes an effective gain of 0 percent on this transaction.