Question

A shopkeeper sells a table at \[8\% \] profit and a chair at \[10\% \] discount, thereby getting Rs. 1008. If he had sold the table at \[10\% \] profit and chair at \[8\% \] discount, he would have got Rs. 20 more. Find the cost price of the table and the list price of the chair.

Answer 1

Hint:
Here we will first assume the cost price of the table and chair to be some variable. Then we will form two equations using the condition given. We will solve these two equations to get the value of the cost price of the table and chair. Then we will find the list price or discounted price of the chair using the cost price.

Complete Step by Step Solution:
Let the cost price of the table be \[x\] and the cost price of the chair be \[y\].
Now we will form the equation using the condition given. It is given that a shopkeeper sells a table at \[8\% \] profit and a chair at \[10\% \] discount, thereby getting Rs. 1008. Therefore, we get
\[\dfrac{{x \times \left( {100 + 8} \right)}}{{100}} + \dfrac{{y \times \left( {100 - 10} \right)}}{{100}} = 1008\]
Now we will simplify this equation, we get
\[ \Rightarrow 108x + 90y = 100800\]
\[ \Rightarrow 6x + 5y = 5600\]……………………….. \[\left( 1 \right)\]
Now we will form the equation from another given condition. It is given that if he had sold the table at \[10\% \] profit and chair at \[8\% \] discount, he would have got Rs. 20 more. Therefore, we get
\[\dfrac{{x \times \left( {100 + 10} \right)}}{{100}} + \dfrac{{y \times \left( {100 - 8} \right)}}{{100}} = 1008 + 20\]
Now we will simplify this equation, we get
\[ \Rightarrow 110x + 92y = 102800\]
\[ \Rightarrow 55x + 46y = 51400\]……………………….. \[\left( 2 \right)\]
Multiplying equation \[\left( 1 \right)\] by 55, we get
\[\left( {6x + 5y} \right) \times 55 = 5600 \times 55\]
\[ \Rightarrow 330x + 275y = 308000\]………………………………..\[\left( 3 \right)\]
Multiplying equation \[\left( 2 \right)\] by 6, we get
\[\left( {55x + 46y} \right) \times 6 = 51400 \times 6\]
\[ \Rightarrow 330x + 276y = 308400\]…………………………………\[\left( 4 \right)\]
Subtracting equation \[\left( 4 \right)\] from equation \[\left( 2 \right)\], we get
\[\begin{array}{l}330x + 275y - \left( {330x + 276y} \right) = 308000 - 308400\\ \Rightarrow 330x + 275y - 330x - 276y = - 400\end{array}\]
Subtracting the like terms, we get
\[ \Rightarrow 0 - y = - 400\]

From the above equation, we get
\[ \Rightarrow - y = - 400\]
\[ \Rightarrow y = 400\]
Now put the value of \[y\] to get the value of \[x\] in equation \[\left( 1 \right)\]. Therefore, we get
\[ \Rightarrow 6x + 5\left( {400} \right) = 5600\]
\[ \Rightarrow 6x + 2000 = 5600\]
Subtracting the like terms, we get
\[\begin{array}{l} \Rightarrow 6x = 5600 - 2000\\ \Rightarrow 6x = 3600\end{array}\]
Dividing 3600 by 6, we get
\[ \Rightarrow x = \dfrac{{3600}}{6} = 600\]
So, the cost price of the table is equal to Rs 600 and the cost price of the chair Rs 400.

Hence the list price of the chair is \[ = 400 \times \dfrac{{90}}{{100}} = {\rm{Rs}}.360\]

Note:
Selling price is the price at which something is sold. Cost price is the cost of producing something or the price at which it is sold without making any money. Profit is the money that you make when you sell something for more than it cost you and loss is the money you make when you sell something for less than it cost you. List price is generally referred to as the discounted amount when a certain percent of discount is applied to the price of the product.