A shopkeeper sells an article for ₹664.2 by giving two successive discounts of 80% and 90% on its marked price. If no discount had been given by him, he would have earned a profit of 64%. Find the cost price of the article (in ₹).

1. A

   20279

2. B

   20285

3. C

   20300

4. D

   20250

Appeared in: DSSSB 6 September 2024

Explanation

• The calculation involves a two-step process: first finding the Marked Price (MP) and then the Cost Price (CP).
• To find the MP, the successive discounts must be reversed from the final Selling Price (SP). The formula is SP = MP × (1 - 0.80) × (1 - 0.90).
• Given SP = ₹664.2, the MP is calculated as ₹664.2 / (0.20 × 0.10) = ₹33,210.
• If no discount is given, the selling price is the MP (₹33,210). A 64% profit on the CP means SP = CP × 1.64.
• The Cost Price is then found by dividing the new SP by the profit factor: CP = ₹33,210 / 1.64 = ₹20,250.

Why Other Options Were Wrong

• Option A: This value is the result of a miscalculation. It does not align with the correct application of the formulas for successive discounts and profit.
• Option B: This is an incorrect value obtained through calculation errors, possibly by incorrectly applying the profit percentage or the discount rates.
• Option C: This value is incorrect. It may arise from rounding errors or an incorrect sequence of operations in the calculation.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss with Successive Discounts as background academic context rather than a clinical decision trigger.
• This type of problem is fundamental to understanding the basics of commerce, including pricing strategies, discount structures, and profit margins.
• For anyone in business or retail, being able to work backwards from a sale price to the original cost is a critical skill for inventory management and financial analysis.
• What if? If the profit had been 100% (i.e., the selling price was double the cost price), the Cost Price would have been ₹33,210 / 2 = ₹16,605. This shows how significantly the profit margin affects the cost.

How to Approach the Question

• First, identify all the given values: the final selling price (SP = ₹664.2), the two successive discount percentages (d1 = 80%, d2 = 90%), and the profit percentage if sold at the marked price (Profit = 64%).
• Recognize that this is a two-step problem. You must first find the Marked Price (MP) before you can find the Cost Price (CP).
• Set up the equation for successive discounts: SP = MP × (1 - d1/100) × (1 - d2/100).
• Substitute the known values into the formula: 664.2 = MP × (1 - 0.80) × (1 - 0.90). Solve for MP.
• Once you have the MP, use the second piece of information. 'If no discount had been given' means the new selling price is the MP you just calculated.
• Use the profit formula, SP = CP × (1 + Profit/100), to find the final answer. Rearrange it to CP = SP / (1 + Profit/100) and substitute the MP as the SP.

Concept Tested & Keywords

• Concept Tested: Profit and Loss with Successive Discounts
• Stem keywords: shopkeeper, sells, successive discounts, marked price, profit, cost price
• Lead-in keywords: Find
• Negative lead-in flag: false

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