Profit, Loss, Faulty measurements

algebra-precalculus

Say, the trader thinks that he is trading $x$ m of cloth with the customer for $\$y.$

  • So, the trader thinks that the wholesale rate is $\displaystyle\frac{\$\frac{10y}{11}}{\frac{10x}9\textrm m}=\frac{\$9y}{11x\:\textrm m}.$

    So, the actual wholesale rate is $\displaystyle\frac{\$9y}{11x\:\textrm m}\div0.8=\frac{\$45y}{44x\:\textrm m}.$

  • So, the trader is actually handing $1.2x$ m of cloth to the customer.

Therefore, the trader is making a loss of $$(1.2x\:\textrm m)\frac{\$45y}{44x\:\textrm m}-\$y=$\frac{5y}{22},$$ i.e., a percentage loss of $$\frac{\frac{5y}{22}}{y+\frac{5y}{22}}=18.519\%.$$

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