A shopkeeper allows a discount of 25 percent on the marked price of an article and, at that discounted selling price, he suffers a loss of 15 percent. What would be his profit percentage if he sells the article at the full marked price without any discount?

Introduction / Context:
This question connects discount, loss, and profit. The shopkeeper initially gives a discount on the marked price and ends up making a loss. We must then determine what would happen if he did not give any discount and sold at the full marked price. This involves relating marked price, selling price after discount, cost price, and then recalculating profit when selling at the marked price.

Given Data / Assumptions:

• Discount on marked price is 25 percent.
• At the discounted price, there is a loss of 15 percent.
• The cost price remains the same in both scenarios.
• We must compute the profit percentage if the article is sold at marked price.
• Percentages are with respect to cost price when speaking of profit or loss.

Concept / Approach:
Let the marked price be M. The discount of 25 percent means the selling price with discount is 75 percent of M. This discounted selling price produces a loss of 15 percent, so it must be 85 percent of the cost price C. Using these relationships, we can express cost price in terms of the marked price. Then we can compute profit when selling at the full marked price M by comparing M with C, using the standard profit percentage formula.

Step-by-Step Solution:
Let marked price be M rupees.After 25 percent discount, selling price S1 equals 0.75 * M.This S1 corresponds to a loss of 15 percent, so S1 equals 0.85 * C where C is the cost price.Therefore 0.75 * M equals 0.85 * C.Cost price C equals (0.75 / 0.85) * M.Now consider selling at full marked price M. Profit then equals M minus C.Substitute C: profit equals M minus (0.75 / 0.85) * M.So profit equals M * (1 minus 0.75 / 0.85) which simplifies to M * ((0.85 minus 0.75) / 0.85) equals M * (0.10 / 0.85).Profit percentage equals (profit divided by C) * 100 which simplifies to (0.10 / 0.75) * 100, approximately 13.33 percent.

Verification / Alternative check:
We can choose a convenient value for the marked price to verify. Let M equal 100 rupees. Then discounted selling price S1 equals 75 rupees. If this is 85 percent of C, then C equals 75 / 0.85 which is about 88.24 rupees. Profit at full marked price is 100 minus 88.24 equals 11.76 rupees. The profit percentage is 11.76 divided by 88.24 multiplied by 100, which is about 13.33 percent. This numerical verification agrees with the algebraic result.

Why Other Options Are Wrong:
Value 11.76 is the profit in rupees from the example with M equal to 100, not the profit percentage. Options 12.12 and 14.28 percent arise from misplacing terms when simplifying ratios or from using the wrong base in percentage calculations. Only 13.33 percent correctly captures the ratio of profit to cost price when the article is sold at the full marked price.

Common Pitfalls:
Many learners confuse which amount is considered as base for different percentages. Loss percentage is based on cost price, while discount percentage is based on marked price. Another common mistake is to subtract or add percentages directly without translating them into actual amounts relative to a chosen base. Setting up equations systematically with variables M and C and then simplifying is the safest method to avoid these errors.

Final Answer:
If the article is sold at the full marked price, the shopkeeper makes a profit of approximately 13.33 percent.