Question

Find the cost price of an article if its selling price (S.P) = Rs. 13230 and discount = $5\dfrac{1}{2}\%$?

Answer 1

Hint: Assume the cost price (C.P) of the article as x. Now, find the discount on the cost price of this article by calculating $5\dfrac{1}{2}\%$ of x. Subtract this amount from the total C.P assumed and equate it with the given selling price (S.P). Calculate the value of x to get the answer. Convert the mixed fraction of discount into the improper fraction by using the conversion formula $a\dfrac{b}{c}=a+\dfrac{b}{c}$.

Complete step-by-step solution:
Here we have been provided with the selling price of an article with a discount of $5\dfrac{1}{2}\%$. We are asked to calculate the cost price of this article.
Let us assume the cost price of the article as x. Now, we know that the discount is given on the cost price and then it is sold at a price known as the selling price. So the discount reduces the selling price of an article. For the above article it is given that the discount percentage is $5\dfrac{1}{2}\%$, converting it into the improper fraction using the conversion $a\dfrac{b}{c}=a+\dfrac{b}{c}$ we get, discount = $\dfrac{11}{2}\%$.
$\Rightarrow $ Price to be reduced = $\dfrac{11}{2}\%\text{ of }\left( x \right)$
$\Rightarrow $ Price to be reduced = $\dfrac{11}{200}\times x$
$\Rightarrow $ The price on which the article is sold = \[\left( x-\dfrac{11x}{200} \right)\]
Now, this price must be equal to the given selling price (Rs. 13230) of the article, so equating the two prices we get,
\[\begin{align}
  & \Rightarrow \left( x-\dfrac{11x}{200} \right)=13230 \\
 & \Rightarrow \dfrac{189x}{200}=13230 \\
 & \Rightarrow x=\dfrac{13230\times 200}{189} \\
\end{align}\]
On simplifying we get,
\[\Rightarrow x=14000\]
Hence, the cost price of the article is Rs. 14000.

Note: Do not calculate the discount on the selling price otherwise you will get the wrong answer. Always remember the conversion relation of mixed fraction and the improper fraction as it is necessary to convert any mixed fraction into the improper fraction for the calculations. You may see that here the cost price turned out to be larger than the selling price that means loss occurred.