Question

A shopkeeper sells a saree at 8% profit and sweater at 10% discount, thereby getting a sum Rs. 1008.If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs. 1028. Find the cost price of the saree and list price (price before discount) of the sweater.

Answer 1

Hint: To solve the question at first we have to consider the cost price of saree and marked price of sweater to be Rs. x and Rs. y respectively. Then we must find out the selling price for saree for 8% profit and the sweater 10% discount and equate their sum with 1008. Thus we will get the first equation in terms of x and y. Then we must find out the selling price for saree for 10% profit and the sweater 8% discount and equate their sum with 1028. Thus we will get the second equation. Finally by solving the two equations obtained we can evaluate x and y. Thus we will get the cost price of the saree and list price of the sweater.

Complete step by step answer:
Let the cost price (CP) of saree and marked price of sweater to be Rs. x and Rs. y respectively
The profit of 8% in saree means for the cost price of Rs. 100 of the saree there is a profit of Rs. 8. Then for the cost price of Rs. x, there is a profit of Rs. \[\dfrac{8x}{100}\].
Thus the selling price (SP) of saree for the cost price Rs. x is given by
\[\begin{align}
  & \Rightarrow SP=CP+\Pr ofit \\
 & \Rightarrow SP=x+\dfrac{8x}{100}=\dfrac{108x}{100} \\
\end{align}\]
Similarly the discount of 10% means for the marked price Rs. y the discount is Rs.\[\dfrac{10y}{100}\]. Then the selling price (SP) of the sweater for the marked price (MP) Rs. y is given by,
\[\begin{align}
  & \Rightarrow SP=MP-Discount \\
 & \Rightarrow SP=y-\dfrac{10y}{100}=\dfrac{9y}{10} \\
\end{align}\]
According to first condition he gets total Rs. 1008, then we will get,
\[\Rightarrow \dfrac{108x}{100}+\dfrac{9y}{10}=1008\]
On taking LCM, we get
\[\Rightarrow 108x+90y=100800\]……………………………. (1)
According to second condition,
The profit of 10% means for the cost price Rs. x the discount is Rs.\[\dfrac{10x}{100}\]. Then the selling price (SP) of the sweater for the cost price (CP) is given by,
\[\Rightarrow SP=CP+Discount\]
Putting, values of CP and discount, we get
\[\Rightarrow SP=x+\dfrac{10x}{100}=\dfrac{110y}{100}\]
The discount of 8% means for the cost price Rs. y the discount is Rs.\[\dfrac{8y}{100}\]. Then the selling price (SP) of the sweater for the marked price (MP) Rs. y is given by,
\[\Rightarrow SP=MP-Discount\]
Putting values of MP and discount, we get
\[\Rightarrow SP=y-\dfrac{8y}{100}=\dfrac{92y}{100}\]
Therefore,
\[\Rightarrow \dfrac{110x}{100}+\dfrac{92y}{100}=1028\]
\[\Rightarrow 110x+92y=102800\]……………. (2)
Now subtracting eq. (1) from eq. (2), we will get,
\[\begin{align}
  & \Rightarrow 2x+2y=2000 \\
 & \Rightarrow x+y=1000 \\
\end{align}\]
\[\Rightarrow y=1000-x\]…………………… (3)
Now substituting the value of eq. (3) in eq. (2), we will get,
\[\begin{align}
  & \Rightarrow 110x+92(1000-x)=102800 \\
 & \Rightarrow 110x-92x=102800-92000 \\
 & \Rightarrow 18x=10800 \\
\end{align}\]
\[\Rightarrow x=\dfrac{10800}{18}=600\]……………….. (4)
Therefore the cost price of saree is Rs. 600.
Substituting the value of eq. (4) in eq. (3), we will get,
\[y=1000-600=400\]………………………….. (5)
Therefore the marked price of the sweater is Rs. 400.

Note:
Before solving the question, read the question twice and get all the data and hints provided in the question. In case of profit the selling price is greater than cost price and in case of loss the cost price is greater than the selling price. Always show the amount in rupees if the amount is written in rupees in question. Try not to make any calculation mistakes especially when you take LCM.