Question 1017843: A manufacturer marks his goods 80% above the cost price but gives 5 articles at the cost of 4 and also 10% discount on cash payment. Calculate the profit percent when the customer pays in cash.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the cost.
the retail price is 80% above cost.
this makes the retail price equal to x + .80 * x which makes it equal to 1.8 * x.
the customer buys 5 articles at the price of 4.
the price of 4 articles is 1.8 * x * 4 which is equal to 7.2 * x.
the customer gets a cash discount of 10%, so the customer pays 7.2 * x * .9 = 6.48 * x.
the cost to the seller is 5 * x.
the profit is 6.48 * x - 5 * x = 1.48 * x.
the profit margin is 1.48 * x divided by 5 * x which is equal to .296 which is equal to 29.6%.
the profit percent is equal to 29.6%.
that's your solution.
note that .9 is equal to (1 - .10), therefore, selling at 10% discount off the sale price is equivalent to selling at 90% of the sale price.
let's put this into numbers to see if it makes sense.
assume the cost is 100 dollars.
he marks the goods at 80% above cost.
the good are marked up to 100 + 80 = 180 dollars.
he sells 5 of the articles at the cost of 4.
the sale price is therefore 4 * 180 = 720 dollars.
the customer pays in cash so he gives the customer 10% discount off the 720 dollar sale price.
10% of 720 dollars is 72 dollars.
720 - 72 = 648 dollars.
the final sale price is 648 dollars.
the cost to the seller is 5 * 100 = 500 dollars.
the profit is 648 - 500 = 148 dollars.
the profit margin is 148 / 500 = .296 = 29.6%.
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