A man buys a watch for Rs 1950 in cash and sells it for Rs 2200 at a credit of 1 year. If the rate of interest is 10 percent per annum, what is his effective gain or loss in rupees on this transaction when the time value of money is considered?

Introduction / Context:
This question mixes profit and loss with the time value of money. The watch is bought in cash and sold on credit, so the actual advantage to the seller depends not only on the difference between the nominal selling price and the cost price, but also on the present value of the delayed payment under a given rate of interest. The aim is to compute the true gain in rupees after discounting the future payment back to the present.

Given Data / Assumptions:
- Cost price of the watch = Rs 1950 paid immediately in cash.
- Selling price nominally = Rs 2200, but receivable after 1 year.
- Interest rate = 10 percent per annum (simple interest assumed).
- There are no additional hidden costs.
- We need to find the effective gain or loss in rupees after considering the present value of the future payment.

Concept / Approach:
To compare fairly with the cost price paid today, we must convert the future payment of Rs 2200 into its present value using simple interest discounting. Present value P is given by P = A / (1 + r * t), where A is the future amount, r is the annual interest rate in decimal, and t is the time in years. Once we find the present value of Rs 2200 due after one year, we compare it to the cost price to determine the net gain or loss in rupees.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs 1950. Step 2: Future selling price amount A = Rs 2200 due after 1 year. Step 3: Rate r = 10 percent per annum, time t = 1 year. Step 4: Present value (PV) of Rs 2200 due after 1 year at 10 percent = 2200 / (1 + 0.10 * 1). Step 5: Denominator = 1.10, so PV = 2200 / 1.10 = Rs 2000. Step 6: Effective gain = PV − CP = 2000 − 1950 = Rs 50. Step 7: Therefore the man effectively gains Rs 50 on this transaction.

Verification / Alternative check:
Think in reverse: If the man invests Rs 1950 at 10 percent simple interest for 1 year, it becomes 1950 * 1.10 = Rs 2145. The present value of Rs 2200 one year later is Rs 2000, which is more than Rs 1950. The difference of Rs 50 is the extra benefit he gets beyond the fair time value of his money. This aligns with the computed effective gain of Rs 50.

Why Other Options Are Wrong:
Option gains Rs 55: This would require a different present value or interest rate and does not match the correct discounting at 10 percent.
Option loses Rs 30: Incorrect because the present value is higher than the cost price, so there is a gain, not a loss.
Option gains Rs 30: Underestimates the benefit and conflicts with the accurate calculation shown above.

Common Pitfalls:
Many learners simply subtract 1950 from 2200 and claim a profit of Rs 250 without adjusting for the delayed payment. Others may apply interest incorrectly or on the wrong base amount. Always discount future amounts back to the present when comparing with an immediate cash payment, and then compute the difference to determine the true gain or loss.

Final Answer:
The man effectively gains Rs 50 on the transaction.