At a 30% discount, the selling price of an article is Rs 1050.\nIf instead the shopkeeper had offered a discount of 15% on the same marked price, what would the new selling price (in rupees) have been?

Introduction / Context:
This question tests understanding of how the selling price changes when the discount rate on the same marked price is altered. First we know the selling price when a 30% discount is offered. From that we infer the marked price. Then we recalculate the selling price using a different discount of 15% on the same marked price. It is a standard exercise in profit and loss and discount topics, and it helps students practice moving backwards from selling price to marked price and then forwards again with a new discount.

Given Data / Assumptions:

• When the discount rate is 30%, the selling price is Rs 1050.
• The discount is on the marked price of the article.
• The marked price remains the same in both cases.
• We want the selling price when the discount rate is 15% on that same marked price.
• No additional taxes or charges are involved.

Concept / Approach:
The discount percentage indicates how much of the marked price is removed. If the discount is 30%, the selling price is 70% of the marked price. Therefore we can write the given selling price as 70% of the marked price and solve for the marked price. After finding the marked price, we then compute 85% of it (since a 15% discount means the customer pays 85% of the marked price) to obtain the new selling price. This two stage approach is systematic and avoids guesswork.

Step-by-Step Solution:
Step 1: Let the marked price be M. Step 2: A discount of 30% means the customer pays 70% of M, that is 0.70 * M. Step 3: Given that at 30% discount, the selling price is Rs 1050, so 0.70 * M = 1050. Step 4: Solve for M: M = 1050 / 0.70. Step 5: 1050 / 0.70 is equal to 1050 * (10 / 7) = 1500, so the marked price is Rs 1500. Step 6: Now consider a discount of 15%. Then the customer pays 85% of the marked price, or 0.85 * M. Step 7: New selling price = 0.85 * 1500 = 1275. Step 8: Therefore, with a 15% discount, the article would sell for Rs 1275.

Verification / Alternative check:
As a quick verification, we can check that a 30% discount on Rs 1500 indeed gives the original selling price. Thirty percent of 1500 is 0.30 * 1500 = 450. Subtracting this from 1500 yields 1500 - 450 = 1050, which matches the given selling price at 30% discount. Similarly, 15% of 1500 is 225. Subtracting this from 1500 gives 1275, which is consistent with our computed new selling price. Both checks agree with the data, confirming the solution.

Why Other Options Are Wrong:
If we choose 1200, that would correspond to paying 80% of the marked price, effectively a 20% discount, not 15%. A selling price of 1175 does not match any simple percentage of 1500 and is therefore inconsistent with the given discount rate. A price of 1100 is even lower and would reflect a discount higher than 26%, not 15%. Only 1275 corresponds exactly to a 15% discount on 1500, so the other options are not correct.

Common Pitfalls:
A common error is to apply the new discount rate directly to the old selling price rather than to the marked price. Another mistake is to subtract the difference between discount percentages from the old selling price, which is not correct because the base value for the percentage remains the marked price. The safest method is always to recover the marked price first from the initial data and then apply the new discount properly to that same marked price.

Final Answer:
The selling price with a 15% discount on the same marked price is Rs 1275.