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dto on "Gross-Profit Ratio Analysis HELP!!!"

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As I was working through this practice problem I got a little confused on the solution compared to my actual understanding of the concept...

Here is the problem: adjustment entry-"Sales reported after year-end that should have been reported before year-end"
-What occurs to Gross Profit Ratio?

Cost of Sales(Debit) 90
A/R(Debit) 100
Sales(Credit) 100
Inventory(Credit) 90

Solution provided by book: Gross Profit Ratio Increases; Gross Profit ratio will always increase when the net change in sales minus cost of goods is positive. (100 Sales - 90 COGS = 10)

My Reasoning: Shouldn't the change in Sales be allocated to the denominator(sales) as well thus leading to a decrease???
For example:
1.Original numbers: (500 Sales - 100 COGS) divided by 500 = 80%
2. Use of adjustment entries: (500 Sales + 100 Sales adj) - (100 COGS + 90 COGS adj) divided by (500 Sales + 100 Sales) = 68.3%

Someone please provide some thought and reasoning on this problem. I am confused if I am right or the book is right or if I should follow the books method or mine!


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