Question Number 7901 by tawakalitu last updated on 24/Sep/16
$${A}\:{dealer}\:{sold}\:{a}\:{car}\:{to}\:{a}\:{man}\:{and}\:{made}\:{a}\:{profit}\:{of}\:\mathrm{15\%} \\ $$$${the}\:{man}\:{then}\:{sold}\:{it}\:{to}\:{a}\:{woman}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${at}\:{a}\:{loss}\:{of}\:\mathrm{5\%}.\:{How}\:{much}\:{did}\:{the}\:{dealer}\:{buy}\:{the}\:{car}. \\ $$
Answered by sandy_suhendra last updated on 24/Sep/16
$${the}\:{man}\:{buys}\:{the}\:{car}\:=\:\frac{\mathrm{100}}{\mathrm{95}}×\mathrm{120},\mathrm{175}=\:\mathrm{126},\mathrm{500}\:={the}\:{dealer}\:{sold} \\ $$$${the}\:{dealer}\:{buys}\:=\:\frac{\mathrm{100}}{\mathrm{115}}×\mathrm{126},\mathrm{500}\:=\:\mathrm{110},\mathrm{000} \\ $$$$ \\ $$
Commented by tawakalitu last updated on 24/Sep/16
$${thanks}\:{for}\:{your}\:{help} \\ $$
Answered by Rasheed Soomro last updated on 24/Sep/16
$${Let}\:{the}\:{dealer}\:{bought}\:{the}\:{car}\:{in}\:{x} \\ $$$${Dealer}\:{sold}\:{the}\:{car}\:\:\:\:{x}+\mathrm{15\%}\:{of}\:{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={x}+\frac{\mathrm{15}}{\mathrm{100}}×{x}={x}+\frac{\mathrm{3}{x}}{\mathrm{20}}=\frac{\mathrm{23}{x}}{\mathrm{20}} \\ $$$${The}\:{man}\:{bought}\:{the}\:{car}\:{in}\:\:\frac{\mathrm{23}{x}}{\mathrm{20}} \\ $$$${He}\:{sold}\:{the}\:{car}\:{at}\:\mathrm{5\%}\:{loss}:\:\:\frac{\mathrm{23}{x}}{\mathrm{20}}−\frac{\mathrm{23}{x}}{\mathrm{20}}×\frac{\mathrm{5}}{\mathrm{100}}=\frac{\mathrm{23}{x}}{\mathrm{20}}−\frac{\mathrm{23}{x}}{\mathrm{400}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{460}{x}−\mathrm{23}{x}}{\mathrm{400}}=\frac{\mathrm{437}{x}}{\mathrm{400}} \\ $$$${He}\:{sold}\:{the}\:{car}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${So},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{437}{x}}{\mathrm{400}}=\mathrm{120},\mathrm{175}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{120175}×\mathrm{400}}{\mathrm{437}}=\mathrm{110000} \\ $$$${The}\:{dealer}\:{bought}\:{the}\:{car}\:{in}\:\mathrm{110},\mathrm{000} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$
Commented by tawakalitu last updated on 24/Sep/16
$${thanks}\:{so}\:{much}.\:{i}\:{appreciate}. \\ $$