after allowing 12% on the marked price a dealer still gains 21% by what percent is the marked price above the cost price
12% off means 88% of the price. So,
.88p = 1.21c
p = 1.375c
so, the marked price is 37.5% above cost
To find the percentage by which the marked price is above the cost price, we need to determine the actual percentage gain made by the dealer.
Let's assume the cost price of the item is C.
After allowing a discount of 12% on the marked price, the selling price becomes (100% - 12%) = 88% of the marked price.
Therefore, the selling price is (88/100) * marked price = 0.88 * marked price.
Since the dealer still gains 21% on the cost price, the selling price is (100% + 21%) = 121% of the cost price.
Therefore, the selling price is 1.21 * C.
Since the selling price is the same in both cases, we can equate the two expressions:
0.88 * marked price = 1.21 * C
To find the percentage by which the marked price is above the cost price, we need to find the ratio:
(marked price - cost price) / cost price * 100%
Substituting the equation we obtained earlier:
(0.88 * marked price - C) / C * 100%
Now, we can solve for the marked price ratio. First, let's isolate the marked price:
0.88 * marked price = 1.21 * C
Divide both sides by 0.88:
marked price = (1.21 * C) / 0.88
Substituting back into the expression:
((1.21 * C) / 0.88 - C) / C * 100%
Simplifying further:
((1.21 - 0.88) * C) / 0.88 * 100%
(0.33 * C) / 0.88 * 100%
(0.375 * C) * 100%
37.5% * C
Therefore, the marked price is 37.5% above the cost price.