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Question Number 177179 by Mastermind last updated on 01/Oct/22

$$\mathrm{If}\mathrm{a}\mathrm{number}\mathrm{is}20\mathrm{\%}\mathrm{more}\mathrm{the}\mathrm{other},\mathrm{how}$$$$\mathrm{much}\mathrm{percent}\mathrm{is}\mathrm{the}\mathrm{second}\mathrm{number}$$$$\mathrm{less}\mathrm{than}\mathrm{the}\mathrm{first}.$$$$$$$$\mathrm{please}\mathrm{help}!$$

Commented by Frix last updated on 02/Oct/22

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{simply}\mathrm{multiplying}\mathrm{and}\mathrm{dividing}$$$$x+20\mathrm{\%}=y\stackrel{1+\frac{20}{100}=1.2}{\iff }1.2x=y$$$$\Rightarrow$$$$x=\frac{y}{1.2}\iff x=.8\overline{3}y\stackrel{1-\frac{16.\overline{6}}{100}=.8\overline{3}}{\iff }y-16.\overline{6\mathrm{\%}}=x$$

Answered by JDamian last updated on 01/Oct/22

$$b=a+a\frac{20}{100}=1.2a$$$$$$$$\frac{b-a}{b}\times 100=\frac{1.2a-a}{1.2a}\times 100=$$$$=\frac{1.2-1}{1.2}\times 100=\frac{0.2}{1.2}\times 100=\frac{20}{1.2}=16.\widehat{6\mathrm{\%}}$$

Commented by Mastermind last updated on 02/Oct/22

$$\mathrm{correct}\mathrm{that}\mathrm{what}\mathrm{i}\mathrm{got}\mathrm{here},\mathrm{thanks}\mathrm{man}$$

Commented by peter frank last updated on 02/Oct/22

$$\mathrm{thanks}$$

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