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Question
In a certain store, the profit is 320% of the cost. If the cost increases 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
30%
70%
100%
250%
None of these
ANSWER : 2
Descrption
<p>This is a math problem that can be solved by using algebra. Let us assume that the cost of the item is <strong>c</strong> and the selling price is <strong>s</strong>. Then, the profit is <strong>s - c</strong> and the profit percentage is <strong>(s - c) / c * 100</strong>. Given that the profit is 320% of the cost, we can write:</p><p><strong>(s - c) / c * 100 = 320</strong></p><p>Solving for <strong>s</strong>, we get:</p><p><strong>s = 4.2c</strong></p><p>Now, if the cost increases by 25%, the new cost is <strong>1.25c</strong>. The selling price remains constant, so the new profit is <strong>s - 1.25c</strong> and the new profit percentage is <strong>(s - 1.25c) / (1.25c) * 100</strong>. Substituting <strong>s = 4.2c</strong>, we get:</p><p><strong>(4.2c - 1.25c) / (1.25c) * 100 = 236</strong></p><p>Therefore, the new profit percentage is approximately <strong>236%</strong> of the new cost.</p><p>To find the percentage of the selling price that is the profit, we can divide the profit by the selling price and multiply by 100. That is:</p><p><strong>(s - 1.25c) / s * 100</strong></p><p>Substituting <strong>s = 4.2c</strong>, we get:</p><p><strong>(4.2c - 1.25c) / (4.2c) * 100 = 70.24</strong></p><p>Therefore, the profit is approximately <strong>70.24%</strong> of the selling price.</p><p>I hope this helps you understand how to solve this problem. </p>
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