A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices and claims that the final price of these items is 50% off the original price. As a percentage of the original price, what is the difference between the true discount and the merchant's claimed discount?

tertre
Apr 16, 2018

#1**0 **

Let the original average price of one item =$100

$100 x 0.7 =$70 - price after 30% original discount.

$70 x 0.8 =$56 - price after the 2nd 20% discount.

$100 - $56 =$44 - The final amount of discount after the 30% and 20% sale.

$44 / $100 =0.44 x 100 **=44% - the true discount compared to the mercant's claim.**

Guest Apr 16, 2018

#3**+2 **

Call the original price of the goods, P

After a 30% discount the price is .7P

And...after a 20% discount on this the final price is (.7P) (.8) = .56P

So...the discount is just [ P -.56P] = .44P

And the merchant's claimed discount is .50P

So....the difference between the true discount and merchant's claimed discount is

l .44P - .50P l = l -.06P l = .06P = [ 6 % of the original price ]

CPhill
Apr 16, 2018