Question Number 71439 by Mr. K last updated on 15/Oct/19
$${If}\:{a}\:{seller}\:{could}\:{purchase}\:{goods}\:{at}\:{an} \\ $$$$\mathrm{8\%}\:{lower}\:{price}\:{by}\:{keeping}\:{the}\:{selling} \\ $$$${price}\:{fixed},\:{his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%.\:{So},\:{what}\:{is} \\ $$$${the}\:{value}\:{of}\:{x}? \\ $$
Commented by ajfour last updated on 16/Oct/19
$${his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%. \\ $$$$\left({its}\:{given}\:{so}\:{in}\:{question}\right) \\ $$$${c}_{{new}} =\left(\mathrm{100\%}−\mathrm{8\%}\right){c}=\mathrm{0}.\mathrm{92}{c} \\ $$
Answered by ajfour last updated on 15/Oct/19
$$\:\:\frac{{s}−\mathrm{0}.\mathrm{92}{c}}{\mathrm{0}.\mathrm{92}{c}}−\frac{{s}−{c}}{{c}}=\mathrm{0}.\mathrm{1} \\ $$$${where}\:\:\:{x}=\left(\frac{{s}−{c}}{{c}}\right)×\mathrm{100} \\ $$$$\Rightarrow\:\:\frac{{s}}{{c}}=\frac{{x}}{\mathrm{100}}+\mathrm{1} \\ $$$$\Rightarrow\:\frac{{x}}{\mathrm{100}}+\mathrm{1}−\mathrm{0}.\mathrm{92}−\frac{\mathrm{0}.\mathrm{92}{x}}{\mathrm{100}}=\mathrm{0}.\mathrm{092} \\ $$$$\Rightarrow\:\frac{\mathrm{0}.\mathrm{08}{x}}{\mathrm{100}}=\mathrm{0}.\mathrm{012}\:\:\Rightarrow\:\:{x}=\:\mathrm{15}\:. \\ $$
Commented by Mr. K last updated on 15/Oct/19
$${How}\:{did}\:{you}\:{develop}\:{the}\:{first}\: \\ $$$${expression}? \\ $$
Commented by ajfour last updated on 15/Oct/19
$${p\%}=\frac{{s}−{c}}{{c}}×\mathrm{100} \\ $$$${new}\:{cost}\:{price}\:=\:\frac{\mathrm{92}}{\mathrm{100}}×{c}\:=\:\mathrm{0}.\mathrm{92}{c} \\ $$$${new}\:{p\%}−{old}\:{p\%}=\mathrm{10} \\ $$$$\Rightarrow\:\:\left(\frac{{s}−\mathrm{0}.\mathrm{92}{c}}{\mathrm{0}.\mathrm{92}{c}}\right)×\mathrm{100}−\left(\frac{{s}−{c}}{{c}}\right)×\mathrm{100}=\mathrm{10} \\ $$$$\Rightarrow\:\frac{{s}−\mathrm{0}.\mathrm{92}{c}}{\mathrm{0}.\mathrm{92}{c}}−\frac{{s}−{c}}{{c}}=\:\mathrm{0}.\mathrm{1}\: \\ $$
Commented by Mr. K last updated on 15/Oct/19
$${What}\:{is}\:{c}? \\ $$
Commented by ajfour last updated on 15/Oct/19
$${cost}\:{price}\:\left({original}\right) \\ $$$${s}\:\left({the}\:{fixed}\:{selling}\:{price}\right) \\ $$$${p}\:{is}\:{profit}. \\ $$
Commented by Mr. K last updated on 15/Oct/19
$${why}\:{new}\:{p\%}−{old}\:{p\%}=\mathrm{10}? \\ $$$${and}\:{how}\:{did}\:{you}\:{find}\:{the}\:{new}\:{cost} \\ $$$${price}? \\ $$