The marked price of an item is Rs. 1,500. Even after giving a 10% discount, the shopkeeper gets a 25% profit. What is the cost price of the item?

1. A

   1,240 रूपये

2. B

   1,090 रूपये

3. C

   1,080 रूपये

4. D

   1,120 रूपये

Appeared in: CGHS SSC - 2018

Explanation

• The first step is to calculate the actual selling price (SP) after the 10% discount is applied to the marked price (MP) of Rs. 1,500. SP = 1500 × (1 - 10/100) = 1500 × 0.90 = Rs. 1,350.
• The problem states that this selling price of Rs. 1,350 includes a 25% profit on the cost price (CP).
• This can be expressed with the formula: SP = CP × (1 + Profit%/100).
• Substituting the known values: 1,350 = CP × (1 + 25/100) = CP × 1.25.
• To find the cost price, we rearrange the formula: CP = 1,350 / 1.25 = Rs. 1,080.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may arise from miscalculating the profit or discount. For example, incorrectly calculating 25% profit on the marked price (0.25 * 1500 = 375) and then subtracting it from the SP (1350 - 375) does not yield a logical result.
• Option B: This is a calculation error. It is close to the correct answer but does not result from the correct application of the formulas for discount and profit.
• Option D: This value is incorrect. It might be obtained by incorrectly applying the percentages. For instance, if one were to subtract the profit percentage from the selling price in a flawed way, a wrong answer like this could be reached.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Cost Price from Marked Price, Discount, and Profit Percentage as background academic context rather than a clinical decision trigger.
• This type of calculation is a fundamental concept in commerce and financial literacy, essential for setting prices, managing a business, and making informed consumer decisions.
• Understanding the difference between marked price, selling price, and cost price helps in analyzing business profitability and sales strategies.
• What if the 25% profit was calculated on the selling price (a profit margin) instead of the cost price (a markup)? The cost price would be different. Profit = 25% of 1,350 = Rs. 337.50. The Cost Price would then be SP - Profit = 1,350 - 337.50 = Rs. 1,012.50. This shows the importance of specifying how profit is calculated.

How to Approach the Question

• First, identify all the given information: Marked Price (MP) = Rs. 1,500, Discount = 10%, and Profit = 25%. The goal is to find the Cost Price (CP).
• Recognize that this is a two-step problem. You cannot directly relate the marked price to the cost price without finding the selling price first.
• Step 1: Calculate the Selling Price (SP). Apply the discount to the marked price. The formula is SP = MP × (1 - Discount%/100).
• Step 2: Use the calculated SP to find the CP. The profit is calculated on the CP. The formula is SP = CP × (1 + Profit%/100).
• Rearrange the formula from Step 2 to solve for the unknown CP: CP = SP / (1 + Profit%/100).
• Substitute the numbers into the formulas and perform the calculations carefully to arrive at the final answer.

Concept Tested & Keywords

• Concept Tested: Calculating Cost Price from Marked Price, Discount, and Profit Percentage.
• Stem keywords: marked price, discount, profit, cost price
• Lead-in keywords: What is
• Negative lead-in flag: false

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