Question

The market price of an article is \[20\% \] above the cost price. A discount of \[10\% \] is allowed to a customer. Find the profit percent.

Answer 1

Hint: Profit is selling price minus cost price. The profit is also known as gain. $ \Pr ofit\% = \dfrac{{\Pr ofit \times 100}}{{C.P.}} $ . Discount is always calculated on the basis of the market price.

Complete step-by-step answer:
Profit and loss are used in finance and business transactions to check whether the business has made a profit or loss during a particular period of account. Certainly it can be done by deducting all the expenditure from total income, the profit or loss of the business.
The market price of an article is 20% above the cost price. A discount of 10% is allowed to a customer.
Let the cost price is x. Therefore, market price is equal to cost price plus 20% of cost price.
Market price is \[x + 20\% \left( x \right) = 1.2x\].
Since the market price of an article is 20% above the cost price, therefore the discount is 10% of market price. Thus, the discount is \[10\% \left( {1.2x} \right) = 0.12x\].
The selling price is market price minus discount.
Thus, the selling price is \[1.2x - 0.12x = 1.08x\].
Profit is selling price minus cost price.
Therefore, Profit percentage is (selling price minus cost price)/cost price.
\[
\Rightarrow {\text{Percentage of profit = }}\left( {\dfrac{{1.08x - x}}{x}} \right) \times 100\% \\
   = \dfrac{{0.08x}}{x} \times 100\% \\
   = 8\% \\
 \]
Hence, the profit percent is 8%.

Note: The discount is always calculated on market price. Always start this type of problems assuming respective variable x or any value such as $ 1,10,100 $ and fetch the relation between the selling price or the cost price which is greater or smaller comparatively.