Question

Due to short supply in market, a shopkeeper marked-up the price of a washing machine by 10% above the printed price. a customer paid Rs. 7,128 for the washing machine inclusive of sale tax at 18%. Find the printed price of the washing machine. If the shopkeeper bought it at 15% discount, find the profit percentage of the shopkeeper.

Answer 1

Step 1: Given information:

The cost price for the customer inclusive of GST$=\mathrm{Rs}.7,128$

Rate of sale tax$=18\%$

Mark-up rate=$=10\%$

Step 2: Calculate the printed price of the washing machine:

Let the printed price be $\mathrm{Rs}.x$.

Since the shopkeeper marked up the price of a washing machine by $10\%$ above the printed price,

$$\begin{gathered} \mathrm{Marked}\mathrm{price}=x+(10\%\mathrm{of}x) \\ \mathrm{Marked}\mathrm{price}=x+\frac{1}{10}x=\frac{11}{10}x \end{gathered}$$

The cost price for the customer inclusive sales tax is computed as:

$\begin{array}{rcl}\mathrm{C}.\mathrm{P}& =& \frac{11}{10}x+\left(18\%\mathrm{of}\frac{11}{10}x\right)\\ & \Rightarrow & \mathrm{C}.\mathrm{P}=\frac{11}{10}x+\left(\frac{18}{100}\times \frac{11}{10}x\right)\\ \therefore \mathrm{C}.\mathrm{P}& =& \frac{11}{10}x\times \frac{118}{100}=\frac{1,298}{1000}x\end{array}$

Since, the customer paid $\mathrm{Rs}.7,128$ for the washing machine inclusive of sales tax.

Therefore,

$$\begin{gathered} \frac{1,298}{1,000}x=7,128 \\ \Rightarrow x=7,128\times \frac{1000}{1,298} \\ \Rightarrow x=\mathrm{Rs}.5,491.5 \end{gathered}$$

So, the printed price of the washing machine is $\mathrm{Rs}.5,491.5$.

Step 3: Calculate the profit percent for the shopkeeper:

The selling price without including GST is computed as:

$$\begin{gathered} \mathrm{S}.\mathrm{P}=7,128\times \frac{100}{118} \\ \mathrm{S}.\mathrm{P}=\mathrm{Rs}.6,040.67 \end{gathered}$$

Since the shopkeeper bought the washing machine at a $15\%$ discount.

So that,

$\begin{array}{rcl}& \Rightarrow & \mathrm{C}.\mathrm{P}=5,491.5-\left(\frac{15}{100}\times 5,491.5\right)\\ & \Rightarrow & \mathrm{C}.\mathrm{P}=5,491.5-823.725\\ & \Rightarrow & \mathrm{C}.\mathrm{P}=\mathrm{Rs}.4,667.77\\ \mathrm{Profit}\%& =& \frac{6,040.67-4,667.77}{4,667.77}\times 100\\ & \Rightarrow & \mathrm{Profit}\%=\frac{1,372.9}{4,667.77}\times 100\\ \therefore \mathrm{Profit}\%& =& 29.41\%\end{array}$

Hence, the printed price of the washing machine is$\mathrm{Rs}.5,491.5$ and the profit percent is $29.41\%$.