Question

The cost price of 20 articles is equal to the selling price of 25 articles. The loss percentage in the transaction is
(a) 40%
(b) 30%
(c) 25%
(d) 20%

Answer 1

Hint:
We solve this problem by using the formula of loss percentage of an article.
We have the formula of loss percentage having cost price C.P and selling price S.P is given as
\[\text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100\]
We use the given condition to find the relation between the cost price and the selling price of the article.

Complete step by step answer:
We are asked to find the loss percentage of the article.
Let us assume that the cost price of one article as \[C\]
Let us assume that the selling price of one article as \[S\]
We are given that the cost price of 20 articles is equal to the selling price of 25 articles.
By converting the above statement into mathematical equation then we get
\[\begin{align}
  & \Rightarrow 20C=25S \\
 & \Rightarrow S=\dfrac{4}{5}C \\
\end{align}\]
Now, let us assume that the loss percentage as \[P\]
We know that the formula of loss percentage having cost price C.P and selling price S.P is given as
\[\text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100\]
By using the above formula to given articles then we get
\[\Rightarrow P=\dfrac{C-S}{C}\times 100\]
Now, by substituting the selling price in terms of cost price in above equation then we get
\[\begin{align}
  & \Rightarrow P=\dfrac{C-\left( \dfrac{4}{5}C \right)}{C}\times 100 \\
 & \Rightarrow P=\dfrac{1}{5}\times 100 \\
 & \Rightarrow P=20\% \\
\end{align}\]
Therefore, we can conclude that the loss percentage of given article is 20 %
So, option (d) is correct answer.

Note:
Students may do mistakes in taking the formula of loss percentage.
We know that in the loss the cost price is greater than the selling price so that the formula will be
\[\text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100\]
But students may assume it in reverse and take the formula as
\[\text{Loss percentage}=\dfrac{S.P-C.P}{C.P}\times 100\]
In this case, we get a negative percentage which is never possible.