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# A shopkeeper sold a TV set for '$₹17940$‘ with a discount of ’$8%$‘ and earned a profit of ’$19.6%$'. What would have been the percentage of profit earned if no discount was offered?

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## Step 1: Find the Marked Price(MP) of TV:$⇒$Let the Marked Price(MP) of the TV set be $₹\mathrm{x}$ Discount offered$=8%$Since, The shopkeeper is offering a discount of '$8%$', the Selling price(SP) of the TV $=92%\mathrm{of}\mathrm{MP}$$\therefore$ SP of TV$=92%\mathrm{of}₹\mathrm{x}$ $=\frac{92\mathrm{x}}{100}$And the SP of TV is given to be $₹17940$ $\therefore \frac{92\mathrm{x}}{100}=17940$ $\mathrm{x}=\frac{17940×100}{92}=₹19500$Step 2: Find the Cost Price(CP) of TV:$⇒\mathrm{Cost}\mathrm{Price}\left(\mathrm{CP}\right)=\frac{100}{100+\mathrm{Profit}%}×\mathrm{SP}$It is given that when the shopkeeper sells the TV for'$₹17940$', he gains a profit of $19.6%$$\therefore$ CP of TV$=\frac{100}{100+19.6}×17940$ $=\frac{100}{119.6}×17940$ $=₹15000$Step 3: Find the Profit:$⇒$It is given that no discount has been offered, So the Selling Price would be equal to the Marked Price(MP), i.e, $₹19500$$\begin{array}{rcl}& ⇒& \mathrm{Profit}=\mathrm{Selling}\mathrm{Price}-\mathrm{Cost}\mathrm{Price}\\ & =& 19500-4500\\ & =& ₹4500\\ & & \end{array}$Step 4: Find the Profit Percentage:$\begin{array}{rcl}& ⇒& \mathrm{Profit}%=\frac{\mathrm{Profit}}{\mathrm{CP}}×100\\ & =& \frac{4500}{15000}×100\\ & =& 30%\end{array}$Therefore, the Profit % is $30%$  Suggest Corrections  0      Similar questions  Explore more