Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

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

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

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

Answered by Don08q last updated on 18/Aug/20

 according to the ratio given, the cost   of material cannot be more than the  labour cost. If it is less instead, then     (7/(5+7+13)) × t = c − 840   ((13)/(5+7+13)) × t = c  ⇒    (7/(13)) = ((c − 840)/c)           7c  =  13c − 10920              c = $ 1,820   total cost of production = $ 1820 +                                                           $ (1820−840)                                                      = $ 2,800

$$\:{according}\:{to}\:{the}\:{ratio}\:{given},\:{the}\:{cost} \\ $$$$\:{of}\:{material}\:{cannot}\:{be}\:{more}\:{than}\:{the} \\ $$$${labour}\:{cost}.\:\boldsymbol{{If}}\:\boldsymbol{{it}}\:\boldsymbol{{is}}\:\boldsymbol{{less}}\:\boldsymbol{{instead}},\:{then} \\ $$$$ \\ $$$$\:\frac{\mathrm{7}}{\mathrm{5}+\mathrm{7}+\mathrm{13}}\:×\:{t}\:=\:{c}\:−\:\mathrm{840} \\ $$$$\:\frac{\mathrm{13}}{\mathrm{5}+\mathrm{7}+\mathrm{13}}\:×\:{t}\:=\:{c} \\ $$$$\Rightarrow\:\:\:\:\frac{\mathrm{7}}{\mathrm{13}}\:=\:\frac{{c}\:−\:\mathrm{840}}{{c}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{7}{c}\:\:=\:\:\mathrm{13}{c}\:−\:\mathrm{10920} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{c}\:=\:\$\:\mathrm{1},\mathrm{820} \\ $$$$\:{total}\:{cost}\:{of}\:{production}\:=\:\$\:\mathrm{1820}\:+ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\$\:\left(\mathrm{1820}−\mathrm{840}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\$\:\mathrm{2},\mathrm{800} \\ $$

Commented by pete last updated on 19/Aug/20

Thank you sir

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com