Question Number 57302 by rajesh4661kumar@gamil.com last updated on 02/Apr/19
Answered by tanmay.chaudhury50@gmail.com last updated on 03/Apr/19
$${profit}={sp}−{cp} \\ $$$$\%{profit}=\frac{{sp}−{cp}}{{cp}}×\mathrm{100} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{100}{sp}}{{cp}}−\mathrm{100} \\ $$$${as}\:{per}\:{question}\:{cp}=\%{profit} \\ $$$${cp}=\frac{\mathrm{100}{sp}}{{cp}}−\mathrm{100} \\ $$$${cp}\left({cp}+\mathrm{100}\right)=\mathrm{100}{sp} \\ $$$${cp}^{\mathrm{2}} +\mathrm{100}{cp}+\mathrm{2500}−\mathrm{2500}=\mathrm{100}{sp} \\ $$$$\left({cp}+\mathrm{50}\right)^{\mathrm{2}} =\mathrm{100}\left({sp}+\mathrm{25}\right) \\ $$$${cp}+\mathrm{50}=\sqrt{\mathrm{100}\left({sp}+\mathrm{25}\right)}\: \\ $$$${cp}=−\mathrm{50}+\sqrt{\mathrm{100}\left({sp}+\mathrm{25}\right)}\: \\ $$$${given}\:\:{sp}=\mathrm{24} \\ $$$${cp}=−\mathrm{50}+\sqrt{\mathrm{100}\left(\mathrm{24}+\mathrm{25}\right)}\: \\ $$$${cp}=−\mathrm{50}+\mathrm{10}×\mathrm{7} \\ $$$${cp}=\mathrm{20} \\ $$