Uma sells an article for Rs 3,400 and earns a profit of 25% on its cost price. If instead she had sold the article for Rs 3,265, what profit percentage would she have obtained?

Introduction / Context:
This profit and loss question is about changing the selling price while the cost price remains the same. When the selling price changes, the profit percentage also changes. The key idea is to first compute the cost price from one known selling price and profit percentage, and then use that cost price to compute a new profit percentage with a different selling price.

Given Data / Assumptions:

• First selling price (SP₁) = Rs 3,400.
• Profit at SP₁ = 25% of cost price.
• Second selling price (SP₂) = Rs 3,265.
• Cost price (CP) of the article remains the same in both cases.
• We need to find the profit percentage at SP₂.

Concept / Approach:
The formula connecting cost price and selling price with profit percentage is SP = CP * (1 + profit%). When the profit percentage is given, we can find CP from SP. Afterwards we use the same CP with the new SP to compute profit% again using profit% = (SP - CP) / CP * 100. Understanding that CP does not change is crucial for solving such problems correctly.

Step-by-Step Solution:
Step 1: Let cost price be CP. Given that SP₁ = 3,400 with 25% profit, so 3,400 = CP * 1.25.Step 2: CP = 3,400 / 1.25 = 2,720.Step 3: With SP₂ = 3,265, profit₂ = SP₂ - CP = 3,265 - 2,720 = 545.Step 4: Profit percentage at SP₂ = (545 / 2,720) * 100 ≈ 20.04%.Step 5: This is approximately equal to 20%, matching one of the options.

Verification / Alternative check:
Using CP = 2,720, a 20% profit would mean SP = 2,720 * 1.20 = 3,264. The given SP₂ is 3,265, only Re 1 higher, which is within rounding and option approximation. So 20% is the best and correct choice. None of the other options align closely with the computed profit percentage.

Why Other Options Are Wrong:
22%, 27% and 18% differ significantly from the calculated profit of roughly 20%. To reach 22% or 27%, the selling price would need to be much higher. For 18%, the selling price would need to be lower. As these do not fit the actual numbers given, they are incorrect distractors.

Common Pitfalls:
A common mistake is to apply 25% directly on 3,400 or to try to find the second profit without first computing the true cost price. Another error is to treat the difference between 3,400 and 3,265 as directly related to profit percentage without referencing CP. Always anchor all percentage profit calculations to the cost price, not just the selling price differences.

Final Answer:
If Uma had sold the article for Rs 3,265, her profit percentage would have been approximately 20%.