A trader marks his goods so that after allowing a discount of 10% on the marked price he still gains a profit of 15% on his cost price. If an article costs him Rs. 720, what should be the marked price of the article?

Introduction / Context:
This question is about determining the marked price of an article when the shopkeeper wants to allow a fixed discount yet still achieve a desired profit. This reflects a very common real-life pricing strategy in retail stores. In competitive exams, such questions test the ability to combine discount and profit percentage concepts correctly. The method involves first calculating the required selling price for the target profit and then relating that selling price to the marked price through the given discount percentage.

Given Data / Assumptions:
- Cost price (CP) of the article = Rs. 720. - Desired profit percentage = 15% on CP. - Discount on marked price = 10%. - We must find the marked price (MP) of the article.

Concept / Approach:
First we compute the selling price that would give a 15% profit on the cost price using SP = CP * (1 + profit%). After that, we know that this selling price is obtained after giving a 10% discount on the marked price, meaning SP = MP * (1 - discount%). Therefore we can set up the equation MP * 0.90 = required SP and solve for MP. This two-step approach ensures we correctly handle both the desired profit and the offered discount.

Step-by-Step Solution:
Given CP = Rs. 720 and desired profit% = 15%. Required selling price (SP) = CP * (1 + 15/100) = 720 * 1.15. Compute SP: 720 * 1.15 = 720 * (115 / 100) = 828. So, SP must be Rs. 828 to obtain 15% profit. Next, discount on the marked price is 10%, so SP = MP * (1 - 10/100) = MP * 0.90. Thus, 0.90 * MP = 828. MP = 828 / 0.90 = 828 * (10 / 9) = 920. Therefore, the marked price must be Rs. 920.

Verification / Alternative check:
Check discount: 10% of 920 = 0.10 * 920 = 92, so discounted price = 920 - 92 = Rs. 828. Check profit on CP: Profit = 828 - 720 = Rs. 108. Profit% = 108 / 720 * 100 = 15%, exactly as required. Both checks confirm that MP = Rs. 920 is correct.

Why Other Options Are Wrong:
- Rs. 900 and Rs. 880 give lower selling prices after a 10% discount, which lead to profit percentages lower than 15%. - Rs. 820 is even smaller; after a 10% discount, SP would be 738, which is only a 2.5% profit on 720. - Rs. 950 would yield a higher profit percentage than 15%, exceeding the target.

Common Pitfalls:
Students sometimes treat the 10% discount as being applied on cost price rather than on marked price, which is conceptually incorrect. Another mistake is to try to apply profit and discount directly on the same base without separating the two steps. Forgetting to convert percentages into decimal multipliers, like 1.15 and 0.90, can also create algebraic confusion.

Final Answer:
The marked price of the article should be Rs. 920.