Retail pricing with discount and target profit: A shopkeeper wants a net profit of 20% on cost after giving a 10% discount on the marked price. By what percentage should the marked price be set above the cost price so that, after the 10% discount, the selling price still yields exactly 20% profit?

Introduction / Context:This question tests retail arithmetic: how to set a marked price when a fixed percentage discount is promised, yet a desired percentage profit on cost must still be achieved. It is a classic chain-percentage problem that requires linking marked price, discount, selling price, and cost price.

Given Data / Assumptions:

• Desired profit on cost = 20%.
• Discount allowed on marked price = 10%.
• All percentages are simple (not compounding) and applied to their respective bases.

Concept / Approach:Let the cost price (CP) be a convenient base, say CP = 100 units. Then the target selling price (SP) for 20% profit is SP = 120. If the discount is 10% on the marked price (MP), then SP = 0.9 * MP. Solve for MP and compare MP with CP to compute the required markup % on cost.

Step-by-Step Solution:

Verification / Alternative check:Discount 10% on 133.333… gives SP = 120, which is indeed 20% above CP = 100. The arithmetic is consistent in both directions.

Why Other Options Are Wrong:

• 30%, 33%, 33 2/3%, 36%: Each yields a selling price (after 10% discount) that is not exactly 20% above cost.

Common Pitfalls:Confusing discount base (MP) with profit base (CP). Always apply each percentage to its proper base to avoid compounding errors.

Final Answer:33 1/3%