SOLUTION: 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

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%.

RELATED QUESTIONS
If a shopkeeper marks the price of goods 50% more than their cost price and allows a... (answered by Theo)

A trader marked his goods at 20% above the cost price. If he allows his Customer a 10%... (answered by jorel555)

a trader marked his goods at 20% above the cost price if he allows his customer a 10%... (answered by Theo)

A manufacturer sells to a wholesaler at a profit of 20%, the wholesale price to a... (answered by rfer)

A dealer marks his goods 20% above cost,but allows 5% discount to the customer. If he... (answered by Theo,MathTherapy)

A tradesman allows a discount of 15% on the written price. How much above the cost price (answered by MathTherapy)

A dealer allows a discount of 25% on the marked price. How much must he mark his goods... (answered by jorel555,MathTherapy)

Goods cost a merchant $72. At what price would he mark them so that he may sell them at... (answered by thepelster)

Goods cost a merchant $72. At what price should he mark them so that he may sell them at... (answered by stanbon,josmiceli)