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Note: Since i could not copy the text of the question i had to attach it as images.

I have 1 question in my book as below Data Question

The correct answer to this question is 108.7% based on the reasoning explained in the book; it made sense. They have mentioned that If A is the dollar amount in 2007 for Store T, thus in 2008 the dollar amount will be 0.92A. Thus 1/0.92 = 1.0869 = 108.7%

I tried below approach (the answer was wrong) and i wish to understand the gap in my understanding.

% change from 2006-2007 is 17% --> 117% % change from 2007-2008 is -8% --> 109% So (117/109)*100 --> 107.339%

LoveWithMaths
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  • % change from 2006-2007 Why would that even matter for a question that clearly asks about the change between 2007-2008, only? FWIW the technical error is in this part: % change from 2007-2008 is -8% --> 109%. You can't add percentages relative to different bases. – dxiv Sep 22 '18 at 04:20
  • Oh I see. Such a silly one. I am not sure whether i understood your sentence about adding percentages relative to different bases. So is now following correct % change from 2007-->2008 is 100-8=92%. So (100/92)*100 = 108.69 gets me correct answer but is it correct way of doing ? because you mentioned something about adding percentage which i dint understood. – LoveWithMaths Sep 22 '18 at 04:30
  • something about adding percentage which i dint understood Point was that the $,+17%,$ was relative to the 2006 base, while the $,-8%,$ percent was relative to the (different) 2017 base. You can't add them like $,100+17-8=109,$ because the denominators are different. Think for example at what happens if you had $,+50%, -50%,$ instead of $,+17%, -8%,$. So is now following correct Yes. – dxiv Sep 22 '18 at 04:35

1 Answers1

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A drop of $8\%$ of $117\%$ from $117\%$ is $-9.36\% = 107.64\%$.

$$\frac{117}{107.64}\cdot 100 = 108.7\%$$

Phil H
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