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A retailer buys 25 identical items for Rs P and sells some for Rs P. If the profit is calculated as 8% based on the selling price instead of the cost price, how many items were sold?
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Solution: ## Step 1: Understand the given problem\nLet's assume the selling price per item is \$S\$ and the cost price per item is \$C\$. The total cost for 25 items is 25C = P.\n\n## Step 2: Express profit based on selling price\nThe profit percentage based on the selling price is given as 8%, so P = S \u00b7 x, where x is the number of items sold.\n\n## Step 3: Calculate profit and cost relationship\nGiven that profit is 8% of selling price: Profit = 0.08 \u00b7 S \u00b7 x.\n\n## Step 4: Relate cost, selling price, and profit\nSince Cost = 25C and Selling Price = S \u00b7 x = P, and Profit = Selling Price - Cost, we have 0.08Sx = Sx - 25C.\n\n## Step 5: Use given conditions to find relationship between C and S\nFrom 25C = P = Sx, we get C = (Sx) / 25.\n\n## Step 6: Substitute C in terms of S and x in profit equation\nSubstituting C in the profit equation: 0.08Sx = Sx - 25((Sx)/25).\n\n## Step 7: Solve for x\nThis simplifies to 0.08Sx = Sx - Sx, which was incorrectly simplified. Correct approach:\nLet's assume selling price as 100, then CP will be 92. The ratio of (100 / 92) will give the number of items sold.\n\n## Step 8: Correct Calculation\n(100 / 92) = (25 / x)\nx = 23\n\nThe final answer is: 23