Question

A shopkeeper allows \[8\% \] discount on his goods and still earns a profit of \[15\% \] . If an article is sold for Rs. \[460\], find the marked price and the cost price.

Answer 1

Hint: Here we are asked to find the marked price and the cost price by using the given data. To find the value of the marked price we will use the formula which has been given in the formula section that is nothing but the sum of selling price and discount. Then to find the cost price we will use the selling price formula that contains cost price and profit percentage, by modifying it we will find the cost price.
Formula: Formula that we need to know:
Relation between marked price selling price and discount
\[Marked{\text{ }}price = \;selling{\text{ }}price + \;Discount\]
When discount is provided, the marked price is higher than selling price
Relation between selling price and cost price and profit
\[selling\,price = \dfrac{{100 + profit\% }}{{100}} + \cos t\,price\]

Complete step by step answer:
It is given that the price of the article at which it is sold is Rs. \[460\]
(i)
For calculating marked price
Since we know selling price and discount offered we can find marked price
\[Marked{\text{ }}price = \;selling{\text{ }}price + \;Discount\]
But let us calculate discount, it is given that there is \[8\% \] discount
So,
\[discount = \dfrac{8}{{100}} \times 460 \]
\[= 8 \times 4.6 = 36.8 \]
So the discount amount is
\[discount = 36.8\]
Now putting values in marked price formula
\[MP = 460 + 36.8 \]
\[MP = 496.8 \]
So the marked price of an article in which the is \[8\% \] discount is \[496.8\]
(ii)
For calculating cost price
Since we know selling price and profit made we can easily calculate cost price of article by
\[selling\,price = \dfrac{{100 + profit\% }}{{100}} + \cos t\,price\]
There is \[15\% \] profit still made so using the above relation we can find CP (cost price)
\[CP = \dfrac{{100 \times selling\,price}}{{100 + 15}} \]
\[CP = \dfrac{{100 \times 460}}{{115}} = \dfrac{{46000}}{{115}} \]
\[CP = 400 \]
So the cost price is \[400\]

Note:
In order to understand the problem we first need to understand the concept of selling price marked price and cost price and the relation between them along with profit and discount made. Use signs carefully when dealing with profit and discount.