$$a \propto \frac{1}{b}$$

If $a$ increases by 10%, how would one work out the percentage change of $b$, without knowing the value of either variable?

  • $\begingroup$ If $a,b$ change to $a',b'$ then by inverse proportionality $\displaystyle \frac{a'}{a}=\frac{1}{b'} \Big/ \frac{1}{b}=\frac{b}{b'}\,$. Now if $\displaystyle\frac{a'}{a}=110\%=1.1\,$, then $\displaystyle \frac{b'}{b}=\cdots\;$ $\endgroup$ – dxiv Jul 3 '17 at 18:46

Inverse proportion means: $a\cdot b=k$.

Hence: $$1.1a\cdot \frac{1}{1.1}b=k \Rightarrow \frac{1}{1.1}-1=-\frac{1}{11}.$$

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  • $\begingroup$ Great answer. Thank you. $\endgroup$ – Pancake_Senpai Jul 3 '17 at 19:06
  • $\begingroup$ You are welcome. $\endgroup$ – farruhota Jul 3 '17 at 19:08

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