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Q76 (CAPF/2021) Economy › Basic Concepts & National Income › Percentages and profit-loss Answer Verified

In a stock clearance sale, a shopkeeper gives 40% off on all his items. He incurs a loss of 25% by selling an item of marked price 2,000. Which one of the following is the cost price of this item?

Result
Your answer: —  Â·  Correct: C
Explanation

To find the cost price, we first determine the selling price (SP) from the marked price (MP). The shopkeeper offers a 40% discount on the MP of 2,000. Using the formula for sale price, SP = MP × (1 - Discount%) = 2,000 × 0.60 = 1,200. The problem states that at this SP, the shopkeeper incurs a loss of 25%. Loss occurs when the cost price (CP) is greater than the SP. The relationship between CP, SP, and loss percentage is given by SP = CP × (1 - Loss%). Substituting the known values: 1,200 = CP × (1 - 0.25), which simplifies to 1,200 = CP × 0.75. Solving for CP, we get CP = 1,200 / 0.75 = 1,600. Thus, the cost price of the item is 1,600.

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