Question

The list price of an article is Rs 800 and is available at a discount of 15 percent. Find the cost price of the article, if a profit of \[13\dfrac{1}{3}\% \] is made on selling it.

Answer 1

Hint: Here we need to find the cost price of the article. For that, we will first calculate the amount of money discounted for the article using the formula. Then we will calculate the value of the selling price which will be equal to the difference between the marked price and the amount of discount. Then we will use the formula of profit percent and then after substituting all the values we will get the required cost price of the article.

Formula used:
\[{\rm{Profit}}\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100\], where, \[S.P\] refers to the selling price and \[C.P\] refers to the cost price.

Complete step-by-step answer:
Here we need to find the cost price of the article.
It is given that the list price of the article is equal to Rs 800. So,
Marked price of the article \[ = {\rm{Rs}}800\]
Discount percent \[ = 15\% \]
\[{\rm{Profit}}\% = 13\dfrac{1}{3}\% \]
We will first calculate the amount of money discounted for the article which will be equal to the product of the discount percent and the marked price.
\[{\rm{Discount}} = 15\% \times \] marked price
Now, we will substitute the value of the marked price. Therefore, we get
\[ \Rightarrow {\rm{Discount}} = 15\% \times {\rm{800}}\]
Converting percentage into fraction, we get
\[ \Rightarrow {\rm{Discount}} = \dfrac{{15}}{{100}} \times {\rm{800}}\]
On further simplification, we get
\[ \Rightarrow {\rm{Discount}} = 15 \times {\rm{8}}\]
On multiplying the numbers, we get
\[ \Rightarrow {\rm{Discount}} = {\rm{Rs}}120\] ………. \[\left( 1 \right)\]
We will calculate the value of the selling price which will be equal to the difference between the marked price and the discount money.
Selling price \[ = \] Marked value \[ - \] Discount
Now, we will substitute the value of discount and the marked value in the above equation. Therefore, we get
\[ \Rightarrow {\rm{Selling Price}} = 800 - 120\]
On subtracting the numbers, we get
\[\] ……… \[\left( 2 \right)\]
Now, we will use the formula of the profit percent.
Now, we will substitute the value of selling price and the profit percent in the formula \[{\rm{Profit}}\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100\]. Therefore, we get
\[13\dfrac{1}{3} = \dfrac{{680 - C.P}}{{C.P}} \times 100\]
Now, we will first convert the mixed fraction into improper fraction.
\[ \Rightarrow \dfrac{{40}}{3} = \dfrac{{680 - C.P}}{{C.P}} \times 100\]
On cross multiplying the terms, we get
\[ \Rightarrow 40C.P = 68000 \times 3 - 3 \times 100C.P\]
On multiplying the terms, we get
\[ \Rightarrow 40C.P = 204000 - 300C.P\]
On adding and subtracting the like terms, we get
\[\begin{array}{l} \Rightarrow 40C.P + 300C.P = 204000\\ \Rightarrow 340C.P = 204000\end{array}\]
On dividing both sides by 340, we get
\[\begin{array}{l} \Rightarrow \dfrac{{340C.P}}{{340}} = \dfrac{{204000}}{{340}}\\ \Rightarrow C.P = 600\end{array}\]
Hence, the required cost price of the article is equal to \[{\rm{Rs}}.600\]

Note: We need to keep in mind that if the value of the selling price is greater than the cost price then the difference between the selling price and the cost price will give us the profit earned on selling that product. Similarly, if the value of the cost price is greater than the selling price then the difference between the selling price and the cost price will give us the loss incurred on selling that product.