Question

The marked price of an article is Rs. 3500 and the rate of GST is 12%. A shopkeeper allows a discount of 20% and still makes a profit of 10%. Find the original cost price of the article and the selling price including GST.

Answer 1

Hint: Assume the original cost price as x and the selling price including GST as y. Now, in the first step find the net marked price by including the GST of Rs. 3500 in it. To do this add 3500 and 12% of 3500. In the next step consider the discount of 20% on this overall price obtained to get the selling price and therefore the value of y. Now, use the formula profit% = $\left( \dfrac{y-x}{x} \right)\times 100\%$ and substitute the obtained value of y and given profit% to calculate the value of x.

Complete step by step solution:
Here we have been provided with the marked price of an article with the rate of GST as 12% and we are asked to find the original cost price and the selling price including the GST if the discount provided by the shopkeeper is 20% and he is making a profit of 10%.
Let us assume the original cost price as x and the selling price including GST as y. Now, the marked price including the GST will be the sum of Rs. 3500 and 12% of Rs. 3500. So we have,
$\Rightarrow $ Net price of the article = $3500+\left( \dfrac{12}{100}\times 3500 \right)$
$\Rightarrow $ Net price of the article = Rs. 3920
Considering the discount of 20% provided by the shopkeeper on this net price we get the selling price of the article including the GST, so we get,
$\begin{align}
  & \Rightarrow y=3920-\dfrac{20}{100}\times 3920 \\
 & \Rightarrow y=3920-\dfrac{1}{5}\times 3920 \\
\end{align}$
$\Rightarrow $ y = Rs. 3136
Therefore the selling price including the GST is Rs. 3136.
Now, it is given that the shopkeeper makes a profit of 10% on this selling price. We know that the profit% = $\dfrac{\text{profit}}{\text{cost price}}\times 100\%$ where profit = selling price – cost price, so substituting the obtained and the given values we get,
$\begin{align}
  & \Rightarrow 10\%=\dfrac{y-x}{x}\times 100\% \\
 & \Rightarrow \dfrac{1}{10}=\dfrac{3136}{x}-1 \\
 & \Rightarrow \dfrac{1}{10}+1=\dfrac{3136}{x} \\
\end{align}$
On simplifying we get,
$\Rightarrow x=3136\times \dfrac{10}{11}$
$\Rightarrow $ x = Rs. 2850.9

Therefore, the original cost price is nearly Rs. 2851.

Note: You must remember the formulas of profit% and loss% as they are frequently used in the topics of profit and loss. In both the formulas we consider the cost price in the denominator because profit and loss is considered on the cost price and not on the selling price. However the numerator is different in both the cases, in case of profit it is (selling price – cost price) while in case of loss it is (cost price – selling price).