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A manager is reporting results for investors. There are two components that make up his business division: Part($A$)+Part($B$)=Whole($C$), or $A+B=C$.

The manager doesn't want investors to know precisely how large $A$ or $B$ are, for competitive reasons. The manager however, is required to report on key performance measures. Thus, he says:

"$A$ declined 4.5%, while $C$ declined 10.1%"

From this, can we tell what the rate of growth / decline was for $B$?

Hagen von Eitzen
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Phooj
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1 Answers1

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No. We are given $$A+B=C$$ for the old year and $$A\cdot(1-0.045)+B\cdot(1+\tfrac p{100}) = C\cdot (1-0.101)$$ From this we find $$ p={-10.1-5.6\frac AB}$$ but the relative proportions of $A$ and $B$ are unknown ...

However, assuming $A,B$ are positive, we can at least estimate that $B$ declined by at least 10.1%.

Hagen von Eitzen
  • 374,180