A merchant has 1000 kg of sugar 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 merchant has 1000 kg of sugar 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. Here's how:
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Let's denote the amount of sugar sold at 8% profit as 'x' kg and the amount sold at 18% profit as '1000 - x' kg (since the total amount of sugar is 1000 kg).
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According to the problem, the merchant gains 14% on the whole. This means that the weighted average profit of the two parts is 14%. We can express this as follows:
(8% * x + 18% * (1000 - x)) / 1000 = 14%
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Simplifying this equation gives us:
0.08x + 180 - 0.18x = 140
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Solving for 'x' gives us:
0.1x = 40
x = 400
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Therefore, the amount of sugar sold at 18% profit is 1000 - x = 1000 - 400 = 600 kg.
So, the merchant sold 600 kg of sugar at 18% profit.
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