In a certain store, the profit is 320% of the cost. if the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
+33653 Let c be old cost and p be old profit, then
s = p + c where s is selling price.
We are told that p = 3.2c, so s = 3.2c + c or s = 4.2c, so that c = s/4.2
Let nc be the new cost. We are told that nc = 1.25c, which means that nc = 1.25*s/4.2
The selling price is the same, but now: s = np + nc, where np is new profit.
Thus s = np + 1.25s/4.2
Subtract 1.25s/4.2 from both sides
s - 1/25s/4.2 = np
s(1 - 1.25/4.2) = np
np/s = 1 - 1.25/4.2 ≈ 0.702
So the new profit as a percentage of the selling price is approximately 70%
+33653 Let c be old cost and p be old profit, then
s = p + c where s is selling price.
We are told that p = 3.2c, so s = 3.2c + c or s = 4.2c, so that c = s/4.2
Let nc be the new cost. We are told that nc = 1.25c, which means that nc = 1.25*s/4.2
The selling price is the same, but now: s = np + nc, where np is new profit.
Thus s = np + 1.25s/4.2
Subtract 1.25s/4.2 from both sides
s - 1/25s/4.2 = np
s(1 - 1.25/4.2) = np
np/s = 1 - 1.25/4.2 ≈ 0.702
So the new profit as a percentage of the selling price is approximately 70%
