+4622 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?
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.
+129899 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 ]
