A shopkeeper defrauds both the dealer and the customer by measuring weights incorrectly. When he is purchasing items from the dealer, he takes 20% more than the indicated weight and when he is selling them to the customer, he gives 20% less than the indicated weight.If the price that the shopkeeper charges his customer is the same as what the dealer charges the shopkeeper, then what profit percentage does the shopkeeper make?50%30%40%60%None of these
Question
A shopkeeper defrauds both the dealer and the customer by measuring weights incorrectly. When he is purchasing items from the dealer, he takes 20% more than the indicated weight and when he is selling them to the customer, he gives 20% less than the indicated weight.If the price that the shopkeeper charges his customer is the same as what the dealer charges the shopkeeper, then what profit percentage does the shopkeeper make?50%30%40%60%None of these
Solution 1
To find the profit percentage made by the shopkeeper, we need to analyze the situation step by step.
Step 1: Let's assume the dealer sells 100 units of a particular item to the shopkeeper at a certain price.
Step 2: The shopkeeper, being dishonest, takes 20% more than the indicated weight when purchasing from the dealer. So, the shopkeeper actually receives 120 units of the item from the dealer.
Step 3: Now, the shopkeeper sells the same 120 units of the item to the customer. However, the shopkeeper gives 20% less than the indicated weight to the customer. So, the customer actually receives only 96 units of the item.
Step 4: Since the price charged by the shopkeeper to the customer is the same as what the dealer charges the shopkeeper, the shopkeeper's cost price for 120 units is the same as the selling price for 96 units.
Step 5: To calculate the profit percentage, we need to find the difference between the cost price and the selling price, and then express it as a percentage of the cost price.
Step 6: The difference between the cost price and the selling price is 120 - 96 = 24 units.
Step 7: The cost price for the shopkeeper is 120 units, so the profit percentage can be calculated as (24/120) * 100 = 20%.
Therefore, the shopkeeper makes a profit percentage of 20%. None of the given options (50%, 30%, 40%, 60%) match the calculated profit percentage.
Solution 2
To find the profit percentage made by the shopkeeper, we need to analyze the situation step by step.
Step 1: Let's assume the dealer sells 100 units of a particular item to the shopkeeper at a certain price.
Step 2: The shopkeeper, being dishonest, takes 20% more than the indicated weight when purchasing from the dealer. So, the shopkeeper actually receives 120 units of the item from the dealer.
Step 3: Now, the shopkeeper sells the same 120 units of the item to the customer. However, the shopkeeper gives 20% less than the indicated weight to the customer. So, the customer actually receives only 96 units of the item.
Step 4: Since the price charged by the shopkeeper to the customer is the same as what the dealer charges the shopkeeper, the shopkeeper's cost price for 120 units is the same as the selling price for 96 units.
Step 5: To calculate the profit percentage, we need to find the difference between the cost price and the selling price, and then express it as a percentage of the cost price.
Step 6: The difference between the cost price and the selling price is 120 - 96 = 24 units.
Step 7: The cost price for the shopkeeper is 120 units, so the profit percentage can be calculated as (24/120) * 100 = 20%.
Therefore, the shopkeeper makes a profit percentage of 20%. None of the given options (50%, 30%, 40%, 60%) match the calculated profit percentage.
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