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.
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.
Solution
Step 1: Let's assume the cost price of rice A and B are 3x and 2x respectively.
Step 2: The selling price of rice A (after 15% profit) would be 115% of 3x, which is 3.45x.
Step 3: The selling price of rice B (after 10% loss) would be 90% of 2x, which is 1.8x.
Step 4: Now, if the merchant sells equal quantities of both the varieties, the total cost price would be (3x + 2x) = 5x and the total selling price would be (3.45x + 1.8x) = 5.25x.
Step 5: The overall profit or loss made by the merchant can be calculated by subtracting the total cost price from the total selling price. In this case, it would be (5.25x - 5x) = 0.25x.
Step 6: To find the percentage of profit, we divide the profit by the total cost price and multiply by 100. So, the percentage of profit would be (0.25x / 5x) * 100 = 5%.
Therefore, the merchant makes an overall profit of 5% by selling equal quantities of both the varieties of rice.
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