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?

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.