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?
This is a math problem that can be solved by using algebra. Let us assume that the cost of the item is c and the selling price is s. Then, the profit is s - c and the profit percentage is (s - c) / c * 100. Given that the profit is 320% of the cost, we can write:
(s - c) / c * 100 = 320
Solving for s, we get:
s = 4.2c
Now, if the cost increases by 25%, the new cost is 1.25c. The selling price remains constant, so the new profit is s - 1.25c and the new profit percentage is (s - 1.25c) / (1.25c) * 100. Substituting s = 4.2c, we get:
(4.2c - 1.25c) / (1.25c) * 100 = 236
Therefore, the new profit percentage is approximately 236% of the new cost.
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:
(s - 1.25c) / s * 100
Substituting s = 4.2c, we get:
(4.2c - 1.25c) / (4.2c) * 100 = 70.24
Therefore, the profit is approximately 70.24% of the selling price.
I hope this helps you understand how to solve this problem.
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