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Question Number 108725 by pete last updated on 18/Aug/20

$$\mathrm{The}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{profit},\mathrm{cost}\mathrm{of}\mathrm{materials}$$$$\mathrm{and}\mathrm{labour}\mathrm{in}\mathrm{the}\mathrm{production}\mathrm{of}\mathrm{an}\mathrm{article}$$$$\mathrm{is}5:7:13\mathrm{respectively}.\mathrm{If}\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{materials}$$$$\mathrm{is}\mathrm{\$}840\mathrm{more}\mathrm{than}\mathrm{that}\mathrm{of}\mathrm{labour},\mathrm{find}$$$$\mathrm{the}\mathrm{total}\mathrm{cost}\mathrm{of}\mathrm{producing}\mathrm{the}\mathrm{article}.$$

Answered by Don08q last updated on 18/Aug/20

$$accordingtotheratiogiven,thecost$$$$ofmaterialcannotbemorethanthe$$$$labourcost.\mathit{I}\mathit{f}\mathit{i}\mathit{t}\mathit{i}\mathit{s}\mathit{l}\mathit{e}\mathit{s}\mathit{s}\mathit{i}\mathit{n}\mathit{s}\mathit{t}\mathit{e}\mathit{a}\mathit{d},then$$$$$$$$\frac{7}{5+7+13}\times t=c-840$$$$\frac{13}{5+7+13}\times t=c$$$$\Rightarrow \frac{7}{13}=\frac{c-840}{c}$$$$7c=13c-10920$$$$c=\mathrm{\$}1,820$$$$totalcostofproduction=\mathrm{\$}1820+$$$$\mathrm{\$}(1820-840)$$$$=\mathrm{\$}2,800$$

Commented by pete last updated on 19/Aug/20

$$\mathrm{Thank}\mathrm{you}\mathrm{sir}$$

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