At a 10 percent discount, the selling price of an article is Rs 4500. If instead a discount of 27.5 percent is offered on the same marked price, what will be the new selling price?

Introduction / Context:
This problem tests the skill of reversing a discount to find the marked price and then applying a different discount rate. Being comfortable with such two step percentage questions is essential for commerce related aptitude and reasoning tests, where discounts and marked prices are frequently combined.

Given Data / Assumptions:
Selling price with 10 percent discount = Rs 4500. Discount rate 1 = 10 percent. Discount rate 2 = 27.5 percent. Marked price remains unchanged between the two scenarios. We must find new selling price at 27.5 percent discount.

Concept / Approach:
If a discount of 10 percent is given, the selling price is 90 percent of marked price. So marked price equals selling price divided by 0.9. Once the marked price is known, apply the second discount of 27.5 percent, meaning the customer pays 72.5 percent of the marked price. Multiplying marked price by 0.725 gives the new selling price.

Step-by-Step Solution:
Let marked price be M. Selling price with 10 percent discount = M * (1 - 10/100) = 0.9M. We are told 0.9M = 4500. So M = 4500 / 0.9. Compute 4500 / 0.9 = 5000. Now apply 27.5 percent discount on this marked price. Customer pays 72.5 percent, so new selling price S = 0.725 * 5000. Compute 0.725 * 5000 = 3625. Thus the new selling price is Rs 3625.

Verification / Alternative check:
Check logically. With marked price 5000, at 10 percent discount the price is 4500, which agrees with the given data. When discount increases from 10 percent to 27.5 percent, clearly the new price must be lower than 4500. Among the options, 3625 is less than 4500 and matches the exact computation. Other options either do not fit the percentage calculations or form incorrect ratios.

Why Other Options Are Wrong:
For selling price 4000, the implied percent of marked price would be 4000 / 5000 * 100 = 80 percent, which corresponds to a 20 percent discount, not 27.5 percent. Values 3500, 3375, or 3125 correspond to even higher discounts such as 30 percent, 32.5 percent, and 37.5 percent. Only 3625 corresponds to exactly 72.5 percent of 5000, that is 27.5 percent discount.

Common Pitfalls:
One frequent mistake is to apply 17.5 percentage points directly on 4500 instead of returning to the marked price. Another error is to subtract 17.5 percent from 90 percent rather than recomputing the effective percentage paid. Always remember that discounts are calculated on the marked price, so you must adjust the base correctly before and after changing discount rates.

Final Answer:
The selling price of the article at a 27.5 percent discount will be Rs 3625.