Subbu purchases a tape recorder at nine-tenths of its selling price and then sells it at 8% more than its selling price; what is his gain percentage on the cost price?

Introduction / Context:
This problem is a variation on profit and loss where the cost price and selling price are defined in terms of a listed selling price. Subbu first buys the tape recorder cheaper than this selling price and then sells it for more than that selling price. The question asks for his profit percentage based on his actual cost. This type of question helps students understand how to manipulate ratios and percentages even when actual rupee values are not given explicitly.

Given Data / Assumptions:

• Let the listed selling price be S rupees.
• Subbu purchases the tape recorder at 9/10 of S, so his cost price is (9/10) * S.
• He sells it at 8% more than the selling price S, that is at 1.08 * S.
• We need to find the profit percentage based on his cost price.

Concept / Approach:
Profit percentage is calculated as (Profit / Cost Price) * 100. Here, instead of working with actual rupees, we represent everything in terms of S. We compute his cost price, compute his final selling price, take the difference as profit, and then divide this profit by cost price to get the profit percentage. This approach shows that the actual numeric value of S is irrelevant for the percentage as long as cost and selling price are expressed in consistent terms.

Step-by-Step Solution:
Let the given selling price be S rupees.Subbu buys the tape recorder at 9/10 of S, so cost price CP = (9/10) * S = 0.9 * S.He sells it at 8% more than S, so final selling price SP = 1.08 * S.Profit = SP - CP = 1.08 * S - 0.9 * S = 0.18 * S.Profit percentage = (Profit / CP) * 100 = (0.18 * S / 0.9 * S) * 100.Simplify 0.18 / 0.9 = 0.2.Thus profit percentage = 0.2 * 100 = 20%.

Verification / Alternative check:
For a numeric check, choose S as Rs. 1000. Then Subbu purchases the tape recorder at 9/10 of 1000, which is Rs. 900. He sells it at 8% more than 1000, that is 1.08 * 1000 = Rs. 1080. Profit is 1080 - 900 = 180. Profit percentage is 180 / 900 * 100 = 20%. This matches perfectly with the algebraic solution, confirming that the profit percentage is 20% independent of the actual value of S.

Why Other Options Are Wrong:
9% and 10% are significantly smaller than the derived 20% and result from incorrect ratios such as 0.18 divided by 2 or dividing by 1.8 instead of 0.9.

180% is far too large and would require profit to be almost double the cost price, which is not the case here.

Common Pitfalls:
Students sometimes misread the phrase "9/10 of its selling price" and set cost price equal to 9/10 of the final selling price instead of the listed one. Another error is to compare profit with S rather than with the cost price. Remember that profit percentage is always calculated with respect to cost price, not with respect to selling price, unless a question explicitly asks for something else. Carefully expressing both cost and selling prices in terms of S before computing their difference helps avoid such mistakes.

Final Answer:
Subbu gain on the tape recorder is 20% of his cost price.