A shopkeeper has 1000 kg of Tea, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Question
A shopkeeper has 1000 kg of Tea, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Solution
To solve this problem, we can use the concept of weighted averages.
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Let's denote the quantity of tea sold at 8% profit as x kg and the quantity sold at 18% profit as (1000 - x) kg.
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According to the problem, the shopkeeper gains 14% on the whole. This means that the weighted average profit of the two parts is 14%.
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We can set up the following equation to represent this situation:
(8/100)x + (18/100)(1000 - x) = (14/100)*1000
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Simplifying the equation gives:
8x + 18000 - 18x = 14000
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Solving for x gives:
10x = 4000
x = 400 kg
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Therefore, the quantity of tea sold at 18% profit is 1000 - x = 1000 - 400 = 600 kg.
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