A merchant offers a discount of 30% on the list price of an article and as a result incurs a loss of 16% on the cost price. If instead the merchant offers a discount of 20% on the same list price, what percentage profit or loss will be made on the cost price?

Introduction / Context:
This aptitude question tests how to move between list price, cost price, discount percentage and profit or loss percentage. Many competitive exams use this pattern to check whether the candidate can correctly set up equations when both discount and loss or profit are involved. Understanding the relationship between list price, selling price and cost price is essential for solving this kind of profit and loss problem accurately.

Given Data / Assumptions:

• The merchant offers a 30% discount on the list price and then incurs a 16% loss.
• The same article is sold next time with a 20% discount on the list price.
• We assume the list price is L and the cost price is CP.
• We need to find the new profit or loss percentage on cost price when the discount is 20%.

Concept / Approach:
The key idea is to express everything in terms of cost price and list price. Discount is applied on list price to get the selling price. Profit or loss percentage is always calculated on cost price. First we use the case with 30% discount and 16% loss to link cost price and list price. Then we use this relation to find the new selling price with 20% discount and compute the profit or loss percentage on cost price.

Step-by-Step Solution:
Step 1: Let the list price be L.Step 2: With 30% discount, selling price SP1 = 0.70 * L.Step 3: At this selling price, there is a 16% loss, so SP1 = 0.84 * CP.Step 4: Therefore 0.70 * L = 0.84 * CP, so CP = (0.70 * L) / 0.84.Step 5: Simplifying, CP = (70/84) * L = (5/6) * L ≈ 0.8333 * L.Step 6: Now consider discount of 20%. New selling price SP2 = 0.80 * L.Step 7: Profit or loss percentage = (SP2 - CP) / CP * 100.Step 8: Substitute CP ≈ 0.8333L and SP2 = 0.80L: (0.80L - 0.8333L) / 0.8333L * 100 ≈ (-0.0333L / 0.8333L) * 100.Step 9: This ratio is approximately -4%, meaning there is a 4% loss on cost price.

Verification / Alternative check:
We can verify with a convenient numerical value for the list price. Suppose L = 100. Then with 30% discount, selling price is 70. If 70 corresponds to 16% loss, then 70 = 0.84 * CP, giving CP = 70 / 0.84 = 83.33. With 20% discount, selling price becomes 80. The loss is CP - SP2 = 83.33 - 80 = 3.33 on a cost of 83.33, which again gives approximately 4% loss. This numerical check confirms the algebraic calculation and validates the final answer as a loss, not a profit.

Why Other Options Are Wrong:
Option A (14 percent profit) is incorrect because calculations clearly show the selling price with 20% discount is still below the cost price. Option C (26 percent profit) is much too high and ignores the original loss relationship between list price and cost price. Option D (8 percent profit) also assumes that the new selling price exceeds the cost price, which contradicts the computed values. Only option B correctly describes a 4 percent loss relative to cost price.

Common Pitfalls:
A common error is to calculate profit or loss directly from the list price or to mix up the base of percentage calculations. Another frequent mistake is to treat both situations independently without first connecting cost price and list price using the given loss condition. Candidates may also mis-handle the negative sign and interpret a negative percentage as profit instead of loss. Careful stepwise handling of equations avoids these issues.

Final Answer:
The merchant will incur a 4 percent loss when offering a 20% discount on the list price in this situation.