Question

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?

Answer 1

Step 1: Find the Marked Price(MP) of TV:

$\Rightarrow$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 $₹17940$

$\therefore \frac{92\mathrm{x}}{100}=17940$

$\mathrm{x}=\frac{17940\times 100}{92}=₹19500$

Step 2: Find the Cost Price(CP) of TV:

$\Rightarrow \mathrm{Cost}\mathrm{Price}\left(\mathrm{CP}\right)=\frac{100}{100+\mathrm{Profit}\%}\times \mathrm{SP}$

It is given that when the shopkeeper sells the TV for'$₹17940$', he gains a profit of $19.6\%$

$\therefore$ CP of TV$=\frac{100}{100+19.6}\times 17940$

$=\frac{100}{119.6}\times 17940$

$=₹15000$

Step 3: Find the Profit:

$\Rightarrow$It is given that no discount has been offered, So the Selling Price would be equal to the Marked Price(MP), i.e, $₹19500$

$\begin{array}{rcl}& \Rightarrow & \mathrm{Profit}=\mathrm{Selling}\mathrm{Price}-\mathrm{Cost}\mathrm{Price}\\ & =& 19500-4500\\ & =& ₹4500\\ & & \end{array}$

Step 4: Find the Profit Percentage:

$\begin{array}{rcl}& \Rightarrow & \mathrm{Profit}\%=\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\\ & =& \frac{4500}{15000}\times 100\\ & =& 30\%\end{array}$

Therefore, the Profit % is $30\%$