A rice merchant sells two varieties of rice, A and B, the ratio of whose cost prices is 3 : 2. If he sells A at a 15% profit and B at a 10% loss, find the overall profit or loss made by the merchant by selling equal quantities of both the varieties.5% profit7.5% profit2.5% loss13% profit
Question
A rice merchant sells two varieties of rice, A and B, the ratio of whose cost prices is 3 : 2. If he sells A at a 15% profit and B at a 10% loss, find the overall profit or loss made by the merchant by selling equal quantities of both the varieties.5% profit7.5% profit2.5% loss13% profit
Solution
Let's assume that the merchant buys 1 kg each of rice A and B.
Given, the cost price ratio of rice A and B is 3:2. So, let's assume the cost price of rice A is 3x and that of rice B is 2x.
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The merchant sells rice A at a 15% profit. So, the selling price of rice A = cost price + profit = 3x + 15% of 3x = 3x + 0.15*3x = 3.45x
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The merchant sells rice B at a 10% loss. So, the selling price of rice B = cost price - loss = 2x - 10% of 2x = 2x - 0.2*2x = 1.8x
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The total selling price of 1 kg each of rice A and B = selling price of A + selling price of B = 3.45x + 1.8x = 5.25x
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The total cost price of 1 kg each of rice A and B = cost price of A + cost price of B = 3x + 2x = 5x
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The overall profit or loss = total selling price - total cost price = 5.25x - 5x = 0.25x
Since the result is positive, the merchant makes a profit. To find the percentage profit, we use the formula:
Profit % = (Profit / Total Cost Price) * 100 = (0.25x / 5x) * 100 = 5%
So, the merchant makes an overall profit of 5% by selling equal quantities of both the varieties of rice.
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