Question

A shopkeeper buys a certain article for 80 and gives a discount of 25% on the retail selling price. In the process, he makes a profit of Rs. 100. What is the marked sale price of the article?

Answer 1

Hint: Assume the marked sale price of the article as x. Find the selling price after the discount by subtracting 25% of x from x. Use the formula: - profit = selling price – cost price and equate the value of profit as 100, cost price as 80 and form a linear equation in x. Solve for the value of x to get the answer.

Complete step-by-step answer:
Here we have been provided with the cost price of the article and the discount the shopkeeper provides on the marked sale price along with the profit he earns on the article. We have been asked to find the marked sale price of the article.
Now, let us assume the marked sale price of the article as x. It is said that the shopkeeper provides a discount of 25% on this price, therefore we have,
$\Rightarrow $ Selling price of the article = x – 25% of x
$\Rightarrow $ Selling price of the article = $x-\dfrac{25}{100}x$
$\Rightarrow $ Selling price of the article = $\dfrac{3x}{4}$
The given profit on the article is Rs. 100 and the cost price is Rs. 80, so using the formula: - profit = selling price – cost price we get,
$\begin{align}
  & \Rightarrow 100=\dfrac{3x}{4}-80 \\
 & \Rightarrow \dfrac{3x}{4}=180 \\
\end{align}$
Solving for the value of x we get,
$\therefore x=240$
Hence, the marked sale price of the article is Rs. 240.

Note: Remember the formulas: - profit = (selling price – cost price) and loss = (cost price – selling price). You must remember the formulas of profit% and loss% as they are frequently used in the topics of profit and loss. Note that the marked sale price is not the actual selling price of the article because there is some discount applied, so do not consider the marked sale price as the actual selling price. Here the selling price is Rs. 180.