By selling an article for Rs. 595, a trader gains 19%. What would be the trader's gain or loss percentage if the article were instead sold for Rs. 475?

Introduction / Context:
This problem requires finding the cost price from one selling situation and then using it to evaluate another selling situation. First, the article is sold at a known profit percentage, allowing us to compute the cost price. Then, by comparing a different selling price with the same cost price, we determine whether there is a gain or a loss and by what percentage. Such problems directly test understanding of profit and loss definitions and the ability to work backwards.

Given Data / Assumptions:

• When sold for Rs. 595, the trader gains 19%.
• Let the cost price be C.
• In a different scenario, the article is sold for Rs. 475.
• We must determine the new gain or loss percentage compared with C.
• All values are in rupees and there are no additional costs.

Concept / Approach:
A gain of 19% means selling price equals 119% of cost price. Thus, SP1 = 1.19 * C. From this, we can find C by dividing the known selling price by 1.19. After finding C, we compare the new selling price with C. If the new selling price is less than C, it is a loss; if greater, it is a gain. The percentage is always calculated as (difference / cost price) * 100, where difference is profit or loss amount.

Step-by-Step Solution:
Let cost price be C.We have 595 = 1.19 * C (because 19% gain means selling price is 119% of cost).So C = 595 / 1.19.Compute C = Rs. 500.Now, in the second scenario, selling price SP2 = Rs. 475.Compare SP2 with C: 475 is less than 500, so this is a loss.Loss amount = C − SP2 = 500 − 475 = Rs. 25.Loss percentage = (Loss / C) * 100 = (25 / 500) * 100 = 5%.

Verification / Alternative check:
At SP1 = Rs. 595 and C = Rs. 500, profit = 95, which is 19% of 500, so the first scenario checks out.At SP2 = Rs. 475, loss = 500 − 475 = 25, which is exactly 5% of 500.Both calculations agree with the problem statement, confirming the correctness of the result.

Why Other Options Are Wrong:
Gain 5% would imply a selling price greater than the cost price, which contradicts 475 being less than 500.Loss 10% would require a loss of 50, meaning a selling price of 450, not 475.Gain 10% is clearly impossible as the price is below cost.Only loss of 5% fits the calculations.

Common Pitfalls:
A frequent error is to assume 19% of 595 is the profit instead of understanding that 595 itself is 119% of the cost price.Some students compute the percentage based on selling price instead of cost price when evaluating loss.It is also easy to mix up whether the new price represents gain or loss if the cost price is not clearly computed first.

Final Answer:
If the article is sold for Rs. 475, the trader incurs a loss of 5%.