Question

The cost of an article was ₹ \[15,500\]. ₹\[450\] were spent on its repairs. If it is sold for a profit of \[15\% \], find the selling price of the article.

Answer 1

Hint:
We will first find the total cost price of the article. Using this total cost price and the profit percentage, we will find the profit made on selling the product. Finally, we will use the total cost price and the total profit made to find the selling price of the article.

Formula used:
We will use the following formulas:
\[{\text{Profit percentage}} = \dfrac{{{\text{Profit}}}}{{{\text{Total cost}}}} \times 100\]
Profit \[ = \] Selling Price \[–\] Cost Price

Complete Step by step Solution:
The cost of the article is given as Rs \[15,500\]. The amount spent on its repairs is Rs \[450\]. Hence,

Total cost of article \[ = \] Cost of article \[ + \] Amount spent on repairs
Substituting the values in the above equation, we get
\[ \Rightarrow \] Total cost of article \[ = 15,500 + 450\]
Adding the terms, we get
\[ \Rightarrow \] Total cost of article \[ = {\text{Rs}}15,950\]

Now, we will find the profit made on selling the product.

We are given the profit percentage as \[15\% \].
Substituting 15 for profit percentage and 15950 for the total cost in the formula \[{\text{Profit percentage}} = \dfrac{{{\text{Profit}}}}{{{\text{Total cost}}}} \times 100\], we get

\[15 = \dfrac{{{\text{Profit}}}}{{15950}} \times 100\]

On cross multiplication, we get
\[ \Rightarrow 15 \times 15950 = {\text{Profit}} \times 100\]

\[ \Rightarrow {\text{Profit}} = \dfrac{{15 \times 15950}}{{100}}\]
Multiplying the terms in the numerator, we get
\[ \Rightarrow {\text{Profit}} = = \dfrac{{239250}}{{100}}\]
Dividing the terms, we get

\[ \Rightarrow {\text{Profit}} = {\text{Rs}}2392.50\]

We have found the Cost price of the article and the Profit made on selling the product. Now, we will find the Selling price of the article.
Substituting the \[{\text{Profit}} = {\text{Rs}}2392.50\] and cost price \[ = 15950\] in the formula Profit \[ = \] Selling Price – Cost Price, we get

 \[2392.50 = \] Selling price \[ - 15950\]
Adding the like terms, we get
 \[ \Rightarrow \] Selling price \[ = 2392.50 + 15,950 = 18,342.50\]

$\therefore $ The selling price of the article is Rs \[18,342.50\].

Note:
While finding profit, the cost price is subtracted from the selling price since the article is sold for a price greater than what it was bought for. On the other hand, a loss is incurred when an article is sold for a price lesser than what it was bought for. In this case, the selling price is subtracted from the cost price.