1
$\begingroup$

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

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

$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

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

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

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.