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A dishonest shopkeeper employs a faulty weighing machine that shows 1 kg for every 850 grams of actual weight. He marks up his goods by 20% above the cost price. Furthermore, he offers a discount of 10% on the marked price to customers. Determine the shopkeeper's overall percentage profit or loss. A) 22.5% B) 25.0% C) 27.06% D) 28.5%
Correct Answer: C) Let's assume the Cost Price (CP) of 1000 grams of goods is `Rs. 1000`. **Step 1: Calculate the Marked Price (MP).** The shopkeeper marks up the goods by 20% above the cost price. `MP = CP \times (1 + \text{Markup Percentage})` `MP = 1000 \times (1 + 0.20) = 1000 \times 1.20 = Rs. 1200` (for 1000 grams nominal weight). **Step 2: Calculate the Selling Price (SP).** The shopkeeper offers a 10% discount on the marked price. `SP = MP \times (1 - \text{Discount Percentage})` `SP = 1200 \times (1 - 0.10) = 1200 \times 0.90 = Rs. 1080` (for 1000 grams nominal weight). **Step 3: Determine the Actual Cost Price for the goods delivered.** The weighing machine shows 1 kg (1000 grams) for every 850 grams of actual weight. This implies that when a customer pays for 1000 grams, they only receive 850 grams of goods. We need to find the cost of the actual quantity delivered. If the CP of 1000 grams is `Rs. 1000`, Then, the CP of 1 gram is `Rs. 1`. So, the actual cost of 850 grams delivered is `Actual CP = 850 \times 1 = Rs. 850`. **Step 4: Calculate the Overall Profit.** The shopkeeper effectively sells goods that cost him `Rs. 850` for `Rs. 1080`. `Profit = SP - Actual CP` `Profit = 1080 - 850 = Rs. 230`. **Step 5: Calculate the Overall Profit Percentage.** `Profit Percentage = (\text{Profit} / \text{Actual CP}) \times 100\%` `Profit Percentage = (230 / 850) \times 100\%` `Profit Percentage = (23 / 85) \times 100\%` `Profit Percentage \approx 27.0588...\% \approx 27.06\%`. Therefore, the shopkeeper's overall profit percentage is approximately 27.06%.
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