Question

A shopkeeper sells an article for Rs. 21,384 including 12% GST. However, the actual rate of GST is 5%. Find the extra profit made by the dealer.

Answer 1

Step 1:

Given terms:

The selling price of the article including GST$=\mathrm{Rs}.21,384$

Rate of GST charged by the shopkeeper$=12\%$

The actual rate of GST$=5\%$

Step 2:

Calculate list price of the article:

Let $\mathrm{Rs}.x$ be the list price of article.

According to the question,

$\begin{array}{rcl}x+\left(x\times \frac{12}{100}\right)& =& 21,384\\ & \Rightarrow & x+\frac{3}{25}x=21,384\\ & \Rightarrow & \frac{28}{25}x=21,384\\ & \Rightarrow & x=21,384\times \frac{25}{28}\\ & \Rightarrow & x=\mathrm{Rs}.19,092.86\end{array}$

Step 3:

Calculate actual sale price:

When the GST is 5%, the actual sale price is computed as,

$\begin{array}{rcl}\mathrm{Actual}\mathrm{sale}\mathrm{price}& =& \mathrm{List}\mathrm{price}+\left(5\%\mathrm{of}\mathrm{List}\mathrm{price}\right)\\ \mathrm{Actual}\mathrm{sale}\mathrm{price}& =& 19,092.86+\left(19,092.86\times \frac{5}{100}\right)\\ \mathrm{Actual}\mathrm{sale}\mathrm{price}& =& 19,092.86+954.64\\ \mathrm{Actual}\mathrm{sale}\mathrm{price}& =& \mathrm{Rs}.20,047.5\end{array}$

Calculate extra profit.

$\begin{array}{rcl}\mathrm{Extra}\mathrm{profit}& =& \mathrm{Sale}\mathrm{price}\mathrm{charged}\mathrm{by}\mathrm{shopkeeper}-\mathrm{Actual}\mathrm{sale}\mathrm{price}\\ & \Rightarrow & \mathrm{Extra}\mathrm{profit}=21,384-20,047.5\\ \therefore \mathrm{Extra}\mathrm{profit}& =& \mathrm{Rs}.1,336.5\end{array}$

Hence, the extra profit made by the dealer is Rs. 1,336.5.