A shopkeeper gives two successive discounts of 50% and 65% on an article and sells it for ₹788.9. If he had not given any discount, he would have earned a profit of 12%. Find the cost price (in ₹) of the article.

1. A

   4046

2. B

   4007

3. C

   4025

4. D

   3991

Appeared in: DSSSB 12 August 2024

Explanation

• The first step is to calculate the single equivalent discount or the net price factor after two successive discounts of 50% and 65%. The final price is (1 - 0.50) * (1 - 0.65) = 0.50 * 0.35 = 0.175 times the Marked Price (MP).
• Given the final selling price (SP) is ₹788.9, the Marked Price (MP) can be calculated as MP = SP / 0.175 = 788.9 / 0.175 = ₹4508.
• The problem states that if sold with no discount (i.e., at the MP), the profit would be 12%. This means the MP is 112% of the Cost Price (CP).
• To find the Cost Price, we divide the Marked Price by 1.12: CP = ₹4508 / 1.12 = ₹4025.

Why Other Options Were Wrong

• Option A: This value is incorrect. It likely arises from a miscalculation, such as an error in dividing the marked price by the profit factor (1.12).
• Option B: This is an incorrect calculation. It does not represent the correct relationship between the calculated marked price (₹4508) and a 12% profit margin.
• Option D: This value is incorrect. It may result from applying the profit calculation to the wrong base amount, such as the discounted selling price (₹788.9), or incorrectly subtracting the profit percentage from the marked price.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Discounts, Profit and Loss as background academic context rather than a clinical decision trigger.
• While this is a quantitative aptitude question, the underlying concepts are relevant in healthcare management.
• Understanding discounts, pricing, and profit margins is essential for roles in hospital administration, pharmacy management, and procurement of medical supplies and equipment.
• What if the profit was 15% instead of 12%? The Cost Price would be lower. The calculation would be CP = 4508 / 1.15 ≈ ₹3920.

How to Approach the Question

• First, identify the given information: the final selling price (SP = ₹788.9) and two successive discounts (d1 = 50%, d2 = 65%).
• Use the formula for successive discounts to work backward and find the original Marked Price (MP). The formula is SP = MP × (1 - d1/100) × (1 - d2/100). Rearrange it to solve for MP: MP = SP / [(1 - d1/100) × (1 - d2/100)].
• Recognize the condition: 'if he had not given any discount, he would have earned a profit of 12%'. This means if the item was sold at its Marked Price, the profit would be 12%.
• Set the calculated Marked Price as the new Selling Price for the profit calculation.
• Use the profit formula SP = CP × (1 + Profit%/100) to find the Cost Price (CP). Rearrange to solve for CP: CP = SP / (1 + Profit%/100).
• Substitute the values and perform the final calculation to get the cost price.

Concept Tested & Keywords

• Concept Tested: Successive Discounts, Profit and Loss
• Stem keywords: successive discounts, sells it for, profit, cost price
• Lead-in keywords: Find the cost price

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