An item is marked 25% above its cost price. What is the maximum discount percentage that can be allowed so that there is neither profit nor loss?

1. A

   20 percent

2. B

   12.5 percent

3. C

   25 percent

4. D

   33.33 percent

Appeared in: NORCET 3 - 2022 (Shift-2)

Explanation

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• The core condition is 'neither profit nor loss', which means the final Selling Price (SP) must equal the initial Cost Price (CP).
• First, calculate the Marked Price (MP). If the CP is 100, a 25% markup makes the MP 125.
• To get back to the SP of 100 from the MP of 125, a discount of 25 is required (125 - 100 = 25).
• The discount percentage is always calculated on the Marked Price. A discount of 25 on an MP of 125 is (25 / 125) * 100, which equals 20%.

Why Other Options Were Wrong

• Option B: A discount of 12.5% is an incorrect calculation. It would result in a selling price of ₹109.375 (125 - 12.5% of 125), leading to a profit.
• Option C: This is a common error. The 25% is the markup percentage on the Cost Price, not the discount percentage on the Marked Price. The base values (CP vs. MP) are different. Applying a 25% discount on the MP (₹125) would lead to a selling price of ₹93.75, resulting in a loss.
• Option D: A discount of 33.33% is an incorrect calculation. It would result in a selling price of approximately ₹83.34, leading to a significant loss.

Related Visual

• Visual 1: Flowchart - A flowchart illustrating the process: Start with Cost Price (CP) → Add Markup (25%) to get Marked Price (MP) → Subtract Discount (X%) to get Selling Price (SP) → Set SP = CP to find X.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit, Loss, and Discount Calculation as background academic context rather than a clinical decision trigger.
• This question tests basic numeracy and aptitude, which are essential skills for nurses.
• While not a direct clinical calculation, the logical reasoning and percentage skills are used in tasks like calculating drug dosages, understanding statistical data in research, and managing ward supplies.
• What if the item was marked 40% above its cost price? Then MP would be 140. The discount required would be 40. The discount percentage would be (40/140) * 100 ≈ 28.57%.

How to Approach the Question

• First, identify the key terms: Cost Price (CP), Marked Price (MP), Selling Price (SP), and Discount.
• To simplify calculations, assume the Cost Price (CP) is a round number like 100.
• Calculate the Marked Price (MP) by adding the markup percentage to the CP.
• Understand the condition 'neither profit nor loss'. This is the crucial step that tells you the final Selling Price (SP) must be equal to the original Cost Price (CP).
• Calculate the discount amount needed to reduce the MP to the SP (Discount = MP - SP).
• Finally, calculate the discount percentage. Remember to use the Marked Price (MP) as the base for this calculation: Discount % = (Discount / MP) × 100.

Concept Tested & Keywords

• Concept Tested: Profit, Loss, and Discount Calculation
• Stem keywords: marked price, cost price, discount percentage, profit, loss
• Lead-in keywords: maximum discount percentage
• Negative lead-in flag: false

Question ID

Qhtj3PyS9pQ3Ej2t8o2OSa

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