Question

When a discount of $15\%$ is allowed on the marked price of an article, it is sold for Rs. $2975.$
Calculate its marked price. Given that the marked price is $40\%$ above the cost price of the article, calculate:
(i) Its cost price
(ii) The profit in Rs. Made by the sale of the article.

Answer 1

First of all suppose the marked price as “x” and then convert the given word statements in the form of mathematical expression and then calculate the cost price and once the cost price is found find the profit of the sold article.

Complete step by step solution:
Let the marked price be $= x{\text{ Rs}}$
When a discount of $15\%$ is allowed on the marked price of an article, it is sold for Rs. $2975.$
Mathematical expression:
$x - \dfrac{{15x}}{{100}} = 2975$
Simplify and find the value for “x”
$\dfrac{{100x - 15x}}{{100}} = 2975$
Term in division on one side if moved to the opposite side then it is multiplied
$85x = 2975 \times 100 \\\ x = \dfrac{{2975}}{{85}} \\\ x = 3500{\text{ Rs}}{\text{.}} \\\$
Now, we are also given that the marked price is $40\%$ above the cost price of the article
Cost price $\times \left( {1 + \dfrac{{40}}{{100}}} \right) = Marked{\text{ price}}$
Place the values and simplify –
Cost price $= \dfrac{{100}}{{140}} \times 3500$
Cost price $= 2500{\text{ Rs}}{\text{.}}$
Now the profit $= Rs.{\text{ 2975 - 2500 = Rs}}{\text{. 475}}$

Additional Information:
Generally, 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.

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.