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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
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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
 #2
avatar+2766 
+1

Sorry, but that's incorrect.

tertre  Apr 16, 2018
 #3
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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 ]

 

 

cool cool cool

CPhill  Apr 16, 2018
 #4
avatar+2766 
+1

Thanks so much, CPhill!

tertre  Apr 16, 2018
 #5
avatar+1357 
+10

Good job CPhill!!

IAmJeff  Apr 16, 2018

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