SOLUTION: Even after giving a discount of 12%, an article was sold at a profit of 10%. By what percentage the marked price was more than the cost price?

Question 1143323: Even after giving a discount of 12%, an article was
sold at a profit of 10%. By what percentage the marked
price was more than the cost price?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the marked up price.
the sale price is 12% off of marked up price = x = .12 * x = .88 * x.
the profit is 10% of the cost.
let p = the profit and c = the cost.
then p = .10 * c.
profit is equal to revenue minus cost = .88 * x - c.
therefore p = .88 * x - c and also p = .10 * c.
you get .10 * c = .88 * x - c
add c to both sides of this equation to get:
1.10 * c = .88 * x
solve for c to get:
c = .88 * x / 1.10 = .8 * x.
the marked price is equal to x and the cost is equal to .8 * x.
the ratio of the marked price to the cost is x / .8 * x = 1.25 * x
this means that the marked price is 25% higher than the cost.

let's see if this makes sense.

assume the cost is 100.
the marked price is 25% higher than the cost = 125.
the article is sold at a 12% discount from the marked price.
the sale price is therefore .88 * 125 = 110
the profit ratio is equal to the (sale price minus the cost) divided by the cost = (110 - 100) / 100 = 10 / 100 = 10%

i think this looks good.
the marked price is 25% higher than the cost.

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