Question

The profit earned by selling an article for Rs. 832 is equal to its loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
1) Rs. 920
2) Rs. 960
3) Rs. 1060
4) Rs. 1200

Answer 1

Hint: We will start by letting the loss and profit for an article is \[x\]. Form an equation as given in the question that the profit earned by selling an article for Rs. 832 is equal to the loss that occurred when the same article is sold for Rs. 448. After forming an equation, we will find the value of \[x\]. The value of \[x\] represents the profit or loss so, use the selling price and subtract the profit to find the value of the cost price. Next, find the sale price of the article for making a 50% profit.

Complete step-by-step answer:
First, let that the profit represented by selling an article is \[x\] and the loss is also represented by \[x\].
Now, we are given in the equation that the profit has been made when the article is sold for Rs. 832 which is equal to loss incurred when the same article is sold for Rs. 448.
Thus, we will form an equation representing the above data,
We get,
\[ \Rightarrow 832 - x = 448 + x\]
Now, we will simplify the above expression to find the value of \[x\].
We get,
\[
   \Rightarrow - 2x = - 384 \\
   \Rightarrow x = \dfrac{{384}}{2} \\
   \Rightarrow x = 192 \\
\]
Thus, we get the value of \[x\] as Rs. 192.
Next, we know that the profit is made when the article is sold at Rs. 832,
Thus, we can find the cost price of an article as we have got the value of \[x\] also,
Thus, we get,
\[
  {\text{Cost price}} = 832 - 192 \\
   = 640 \\
 \]
Hence, the value of the cost price of an article is Rs. 640.
Next, we will find the sale price of an article by multiplying the cost price with 50%.
Thus, we get,
\[
  {\text{Sale price}} = 640 \times \dfrac{{150}}{{100}} \\
   = 960 \\
\]
Hence, we get the sale price as Rs. 960 for making 50% profit.
Thus, option B is correct.

Note: We have found the sale price for making 50% profit, so we have added 50% in 100% and get the sale price at 150% of the cost price of an article as we have considered 100% as the base. We can also find the value of cost price by putting the value of \[x\] as the loss is incurred when the article is sold for Rs. 448 which implies by adding the value of \[x\] 448 gives us the value of cost price. When the profit is made, we will subtract it from the selling price to find the cost price and when the loss is incurred we will add it in the selling price of an article to find the cost price.