A shopkeeper sells an item for ₹436.80 after giving two successive discounts of 30% and 35% on its marked price. Had he not given any discount, he would have earned a profit of 28%. What is the cost price (in ₹) of the item?

1. A

   797

2. B

   750

3. C

   717

4. D

   777

Appeared in: DSSSB October 2024

Explanation

• The problem requires a two-step calculation: first finding the Marked Price (MP) and then the Cost Price (CP).
• The final selling price (₹436.80) is the result of applying two successive discounts (30% and 35%) to the MP. Reversing this calculation (₹436.80 / (0.70 × 0.65)) gives an MP of ₹960.
• If no discount is given, the selling price equals the MP (₹960).
• A 28% profit on the CP results in this selling price of ₹960.
• To find the CP, we reverse the profit calculation: CP = SP / (1 + Profit Percentage), which is ₹960 / 1.28.
• This calculation yields a Cost Price of ₹750.

Why Other Options Were Wrong

• Option A: This value is incorrect. It likely results from a miscalculation, such as incorrectly applying the discount or profit percentages.
• Option C: This value is incorrect. It may arise from an arithmetic error during the division or multiplication steps required to find the marked price or cost price.
• Option D: This value is incorrect. This could be the result of incorrectly combining the successive discounts (e.g., adding them instead of applying them sequentially).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit, Loss, and Successive Discounts as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and mathematical reasoning, skills that are important for various competitive exams.
• While not a clinical question, the ability to perform multi-step calculations is analogous to calculating medication dosages or fluid balances, which requires precision and attention to detail.
• What if the discounts were applied on the Cost Price instead of the Marked Price? The entire calculation would change, as the base for the discount would be the unknown CP, leading to a different set of equations.

How to Approach the Question

• First, identify all the numerical values given: the final selling price (₹436.80), two successive discounts (30% and 35%), and a profit percentage (28%).
• Recognize that this is a two-step problem. You cannot find the cost price directly. You must first find the marked price.
• Set up an equation to find the Marked Price (MP). The final price is the MP after a 30% discount and then a 35% discount: SP = MP × (1 - 0.30) × (1 - 0.35).
• Substitute the known SP (₹436.80) and solve for MP. You should get MP = ₹960.
• Next, use the second piece of information: if no discount is given, the selling price is the MP (₹960), and this price includes a 28% profit.
• Set up the profit equation: SP = CP × (1 + Profit%). So, 960 = CP × (1 + 0.28).

Concept Tested & Keywords

• Concept Tested: Profit, Loss, and Successive Discounts
• Stem keywords: shopkeeper, sells, item, ₹436.80, successive discounts, 30%, 35%, marked price
• Lead-in keywords: What is
• Negative lead-in flag: false

Question ID

QE_RlMMOpmsrukRhMAQRSp

Copy ID