Question
A trader buys 120 kilograms of rice at a price of ₹45
per kilogram, incurring a total cost for the entire quantity. He decides to sell a certain portion of the rice at a 20% profit while selling the rest at a 10% loss. At the end of the transactions, the trader makes an overall profit of ₹243. Based on this information, calculate how many kilograms of rice were sold at the 20% profit rate.Solution
Let the amount of rice sold at a gain be x kg The amount of rice sold at a loss = (120 – x) kg. Selling Price of rice sold at a gain = 120% of (45×x) = 54x Selling Price of rice sold at a loss = 90% of (120 - x) × 45 Total Cost Price = 120 × 45 = 5400 Total Selling Price = 54x + (120 - x) × 40.5 = 54x + 4860 - 40.5x = 13.5x + 4860 Given, Total Profit = 243 So,13.5x + 4860 = 5643 13.5x = 783 x = 58 kg
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