The difference between the cost price and the sale price of an item is Rs. 240. If the profit percent is 20, what price was the article sold?
A) Rs. 1240
B) Rs. 1340
C) Rs. 1440
D) Rs. 1540
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Hint: Here first we will find the profit earned and then by applying the formula for profit percent we will find the cost price of the article and then wit the help of the given data we will find the selling price of the article.
Profit percent is the percentage of profit gained on cost price by selling a profit.
The formula for profit percent is given by:-
\[{\text{Profit percent}} = \dfrac{{{\text{profit}}}}{{{\text{cost price}}}} \times 100\].
Complete step by step solution:
It is given that is the difference between the cost price and the selling price of an item is Rs. 240.
And since we know that the profit is given by:-
\[{\text{profit}} = {\text{selling price}} - {\text{cost price}}\]
Therefore, \[{\text{profit}} = 240Rs\]
Also it is given that profit percent is 20.
Therefore, applying the formula for profit percent we get:-
\[ {\text{Profit percent}} = \dfrac{{{\text{profit}}}}{{{\text{cost price}}}} \times 100 \]
$\Rightarrow 20 = \dfrac{{240}}{{{\text{cost price}}}} \times 100 $
$\Rightarrow {\text{cost price}} = \dfrac{{240}}{{20}} \times 100 $
On simplifying the above values,
$\Rightarrow {\text{cost price}} = 12 \times 100 $
\[\Rightarrow {\text{cost price}} =Rs.1200 \]
Now putting this value of cost price in the formula of profit we get:-
\[ {\text{profit}} = {\text{selling price}} - {\text{cost price}} \]
$\Rightarrow {\text{240}} = {\text{selling price}} - 1200 $
$\Rightarrow {\text{selling price}} = 1200 + 240 $
$\Rightarrow {\text{selling price}} = 1440Rs $
$\therefore$ The selling price of the article is Rs.1440. Hence, option (C) is the correct answer.
Note:
Profit is the amount of money gained on selling a product such that the selling price of the product is higher than its cost price.
The formula for profit is:-
\[{\text{profit}} = {\text{selling price}} - {\text{cost price}}\]
The student should substitute the values in the above formula to get the selling price of the article.
Profit percent is the percentage of profit gained on cost price by selling a profit.
The formula for profit percent is given by:-
\[{\text{Profit percent}} = \dfrac{{{\text{profit}}}}{{{\text{cost price}}}} \times 100\].
Complete step by step solution:
It is given that is the difference between the cost price and the selling price of an item is Rs. 240.
And since we know that the profit is given by:-
\[{\text{profit}} = {\text{selling price}} - {\text{cost price}}\]
Therefore, \[{\text{profit}} = 240Rs\]
Also it is given that profit percent is 20.
Therefore, applying the formula for profit percent we get:-
\[ {\text{Profit percent}} = \dfrac{{{\text{profit}}}}{{{\text{cost price}}}} \times 100 \]
$\Rightarrow 20 = \dfrac{{240}}{{{\text{cost price}}}} \times 100 $
$\Rightarrow {\text{cost price}} = \dfrac{{240}}{{20}} \times 100 $
On simplifying the above values,
$\Rightarrow {\text{cost price}} = 12 \times 100 $
\[\Rightarrow {\text{cost price}} =Rs.1200 \]
Now putting this value of cost price in the formula of profit we get:-
\[ {\text{profit}} = {\text{selling price}} - {\text{cost price}} \]
$\Rightarrow {\text{240}} = {\text{selling price}} - 1200 $
$\Rightarrow {\text{selling price}} = 1200 + 240 $
$\Rightarrow {\text{selling price}} = 1440Rs $
$\therefore$ The selling price of the article is Rs.1440. Hence, option (C) is the correct answer.
Note:
Profit is the amount of money gained on selling a product such that the selling price of the product is higher than its cost price.
The formula for profit is:-
\[{\text{profit}} = {\text{selling price}} - {\text{cost price}}\]
The student should substitute the values in the above formula to get the selling price of the article.