Anil bought an item with 12 frac{1}{2} % disc | vedclass

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Question

(C) Let the labelled price of the article be $Rs. \, y$.The cost price $(CP)$ of the article is the price after a $12 \frac{1}{2} \%$ discount:$CP = y

Vedclass · Accepted Answer

$34 \frac{2}{7} \%$

Vedclass · Answer

(C) Let the labelled price of the article be $Rs. \, y$.The cost price $(CP)$ of the article is the price after a $12 \frac{1}{2} \%$ discount:$CP = y 	imes \left(1 - \frac{12.5}{100}ight) = y 	imes \frac{87.5}{100} = y 	imes \frac{7}{8} = Rs. \, \frac{7}{8} y$.The selling price $(SP)$ of the article is the price after a $17 \frac{1}{2} \%$ profit on the labelled price:$SP = y 	imes \left(1 + \frac{17.5}{100}ight) = y 	imes \frac{117.5}{100} = y 	imes \frac{47}{40} = Rs. \, \frac{47}{40} y$.Profit = $SP - CP = \frac{47}{40} y - \frac{7}{8} y = \frac{47 - 35}{40} y = \frac{12}{40} y = Rs. \, \frac{3}{10} y$.Percentage profit on the cost price = $\left(\frac{	ext{Profit}}{CP}ight) 	imes 100 = \left(\frac{\frac{12}{40} y}{\frac{7}{8} y}ight) 	imes 100 = \left(\frac{12}{40} 	imes \frac{8}{7}ight) 	imes 100 = \frac{12}{35} 	imes 100 = \frac{240}{7} = 34 \frac{2}{7} \%$.

Anil bought an item with $12 \frac{1}{2} \%$ discount on the labelled price. He sold the item with $17 \frac{1}{2} \%$ profit on the labelled price. What was his percent profit on the price he bought?

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