A man buys a watch for Rs 1950 in cash and sells it for Rs 2200 on a credit of 1 year. If the rate of interest in the market is 10% per annum, then, based on the present worth of Rs 2200, by how much amount does he gain or lose on this transaction?

Introduction / Context:
This question tests the concept of true profit or loss when an item is sold on credit. In aptitude exams, it is common to compare the present worth of a future payment with the actual cash cost price in order to judge whether the seller gains or loses. Here, a man buys a watch for a cash price and sells it on a one year credit. Because money has a time value, the future payment of Rs 2200 is not equal to receiving Rs 2200 in cash today. We must discount the future amount at the given interest rate to find its present worth and then compare it with the cash cost price.

Given Data / Assumptions:

• Cash cost price of the watch = Rs 1950.
• Credit selling price after 1 year = Rs 2200.
• Rate of interest in the market = 10 percent per annum (simple interest).
• We compare present worth of Rs 2200 with Rs 1950 to decide gain or loss.

Concept / Approach:
The key idea is present worth. A future payment of S after t years at simple interest rate r percent per year has present worth given by:
Present worth = S / (1 + r * t / 100) For a one year credit, t = 1. After finding the present worth of Rs 2200, we compare it with the cash cost price. If present worth is greater than cost price, there is a gain equal to that difference. If it is lower, there is a loss.

Step-by-Step Solution:
Step 1: Identify S, r and t. S = 2200, r = 10, t = 1 year. Step 2: Compute present worth of Rs 2200 payable after 1 year. Present worth = 2200 / (1 + 10 * 1 / 100) Present worth = 2200 / (1 + 0.10) Present worth = 2200 / 1.10 Present worth = 2000. Step 3: Compare present worth with cash cost price. Cost price (cash) = 1950. Effective selling price in present terms = 2000. Gain = 2000 - 1950 = 50. Thus he gains Rs 50 on the transaction when we correctly account for the time value of money.

Verification / Alternative check:
We can also think in terms of what amount invested today at 10 percent per year would become Rs 2200 after 1 year. Let P be that amount. Then:
P * (1 + 10 / 100) = 2200 P * 1.10 = 2200 P = 2200 / 1.10 = 2000. So, effectively, he is receiving Rs 2000 today for a watch that cost Rs 1950 in cash. The difference again is Rs 50, confirming the gain.

Why Other Options Are Wrong:
Option B (Gain of Rs 55) assumes a different interest or arithmetic error in discounting the future amount. Option C (Loss of Rs 15) wrongly assumes that cash cost is greater than present worth, which is not true here. Option D (Loss of Rs 45) is also incorrect since we clearly found a gain, not a loss. Option E (No profit no loss) would only be correct if the present worth equaled the cash cost of Rs 1950, which is not the case.

Common Pitfalls:
Many learners mistakenly compare the nominal future selling price of Rs 2200 with the cash cost of Rs 1950 and conclude a gain of Rs 250. This ignores the fact that the Rs 2200 will be received after 1 year and must therefore be discounted. Another common mistake is to wrongly apply simple interest to the cost price instead of discounting the future value. Careful attention to which amount is at present and which is in the future is essential.

Final Answer:
The man makes a Gain of Rs 50 on the transaction when the time value of money is considered at 10 percent per annum.