Cash vs. credit sale with interest: A man buys a watch for Rs. 195 in cash and sells it for Rs. 220 on 1-year credit. If the simple interest rate is 10% per annum, does he gain or lose, and by how much (in rupees)?

Introduction / Context: To fairly compare a cash purchase with a credit sale involving a stated interest rate, convert the credit sale price to its present worth (discounted value) and compare with the cash cost. The difference shows the real profit or loss.

Given Data / Assumptions:

• Cash cost price (CP) = Rs. 195.
• Credit sale price after 1 year = Rs. 220.
• Interest rate r = 10% per annum; time t = 1 year.

Concept / Approach: Present worth PW of the credit price = Future value / (1 + r t). Profit = PW − CP. If positive, it is a gain; if negative, a loss.

Step-by-Step Solution:

Verification / Alternative check: If the buyer invested Rs. 195 at 10%, it would become Rs. 214.5 in a year. Selling effectively for PW Rs. 200 shows a modest gain over CP; the problem, however, uses PW directly as the benchmark.

Why Other Options Are Wrong: Rs. 15 and Rs. 3 do not match the present-worth calculation; “Loses” options invert the sign incorrectly.

Common Pitfalls: Comparing 220 directly to 195 without discounting; using the interest on CP rather than discounting the credit price to present.

Final Answer: Gains Rs. 5