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Question Number 71439 by Mr. K last updated on 15/Oct/19

$$Ifasellercouldpurchasegoodsatan$$$$8\mathrm{\%}lowerpricebykeepingtheselling$$$$pricefixed,hisprofitoverthecost$$$$pricewouldincreasefromthe$$$$currentx\mathrm{\%}to(x+10)\mathrm{\%}.So,whatis$$$$thevalueofx?$$

Commented by ajfour last updated on 16/Oct/19

$$hisprofitoverthecost$$$$pricewouldincreasefromthe$$$$currentx\mathrm{\%}to(x+10)\mathrm{\%}.$$$$\left(itsgivensoinquestion\right)$$$$c_{new}=(100\mathrm{\%}-8\mathrm{\%})c=0.92c$$

Answered by ajfour last updated on 15/Oct/19

$$\frac{s-0.92c}{0.92c}-\frac{s-c}{c}=0.1$$$$wherex=\left(\frac{s-c}{c}\right)\times 100$$$$\Rightarrow \frac{s}{c}=\frac{x}{100}+1$$$$\Rightarrow \frac{x}{100}+1-0.92-\frac{0.92x}{100}=0.092$$$$\Rightarrow \frac{0.08x}{100}=0.012\Rightarrow x=15.$$

Commented by Mr. K last updated on 15/Oct/19

$$Howdidyoudevelopthefirst$$$$expression?$$

Commented by ajfour last updated on 15/Oct/19

$$p\mathrm{\%}=\frac{s-c}{c}\times 100$$$$newcostprice=\frac{92}{100}\times c=0.92c$$$$newp\mathrm{\%}-oldp\mathrm{\%}=10$$$$\Rightarrow \left(\frac{s-0.92c}{0.92c}\right)\times 100-\left(\frac{s-c}{c}\right)\times 100=10$$$$\Rightarrow \frac{s-0.92c}{0.92c}-\frac{s-c}{c}=0.1$$

Commented by Mr. K last updated on 15/Oct/19

$$Whatisc?$$

Commented by ajfour last updated on 15/Oct/19

$$costprice\left(original\right)$$$$s\left(thefixedsellingprice\right)$$$$pisprofit.$$

Commented by Mr. K last updated on 15/Oct/19

$$whynewp\mathrm{\%}-oldp\mathrm{\%}=10?$$$$andhowdidyoufindthenewcost$$$$price?$$

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