Question

# A shopkeeper sells a saree at $8%$ profit and a sweater at a $10%$ discount, thereby, getting a sum of $₹1008$. If she had sold the saree at $10%$ profit and the sweater at $8%$ discount, she would have got $₹1028$. Find the cost price of the saree?

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Solution

## $⇒$Let the Cost Price of the saree be $₹\mathrm{x}$ Let the Cost Price of the Sweater be $₹\mathrm{y}$According to the first condition given in the question:A shopkeeper sells a saree at '$8%$' profit and a sweater at a $10%$ discount.$⇒$The formula for Selling Price(SP), in terms of Cost Price(CP) and Profit%, $\mathrm{SP}=\frac{100+\mathrm{Profit}%}{100}×\mathrm{CP}$$\therefore$The selling price (SP) of the saree$=\frac{100+8}{100}\mathrm{x}=\frac{108\mathrm{x}}{100}$………($1$)$\therefore$The Selling Price(SP) of the sweater$=\mathrm{y}-\frac{10\mathrm{y}}{100}=\frac{90\mathrm{y}}{100}$……….($2$)Now by adding both the equations [$1$] and [$2$], we get.$⇒\frac{108\mathrm{x}}{100}+\frac{90\mathrm{y}}{100}=1008$ $108\mathrm{x}+90\mathrm{y}=100800$……………………………………………($3$)According to the second condition given in the question:A shopkeeper sells a saree at 10% profit and a sweater at an 8% discount,$\therefore$The selling price (SP) of the saree$=\frac{100+10}{100}\mathrm{x}=\frac{110\mathrm{x}}{100}$……………….($4$)$\therefore$The selling price (SP) of the sweater$=\mathrm{y}-\frac{8\mathrm{y}}{100}=\frac{92\mathrm{y}}{100}$…………………($5$)Now by adding both the equations –[$4$] and [$5$], we get,$⇒$$\frac{110\mathrm{x}}{100}+\frac{92\mathrm{y}}{100}=1028$ $110\mathrm{x}+92\mathrm{y}=102800$…………………………………………….($6$)Now by subtracting equation [$3$] from equation [$6$], we get,$⇒2\mathrm{x}+2\mathrm{y}=2000$ $\mathrm{x}+\mathrm{y}=1000$ $\mathrm{y}=1000-\mathrm{x}$………………………………………………….($7$)Now by substituting the value of $\mathrm{y}$ from equation ($7$) in equation ($3$), we get,$\begin{array}{rcl}& ⇒& 108\mathrm{x}+90\left(1000-\mathrm{x}\right)=100800\\ 108\mathrm{x}-90\mathrm{x}& =& 100800-90000\\ 18\mathrm{x}& =& 10800\\ \mathrm{x}& =& ₹600\end{array}$Therefore, the cost price of a saree is $₹600$

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