Question

A man sells 5 identical articles for Rs. 15 and makes a profit of 20%. Find his gain or loss percent, if he sells 8 such articles for Rs. 18.40.

Answer 1

Hint: Assume that the cost price of one article is Rs. x. Now, get the cost price of 5 articles. It is given that the man makes a profit of 20% while selling 5 articles for Rs. 15. The value of profit is 20% of the cost price of 5 articles. Now, use the formula, Selling price = Cost price + profit and calculate the value of x. Using the value of x get the cost price of 8 articles. It is given that the man sells 8 articles at Rs. 18.40. Now, calculate the value of loss using the formula, Loss = Cost price – selling price. Then, solve further to get the percentage of loss by using the formula, \[\dfrac{\text{Loss}}{\text{Cost price}}\text{ }\!\!\times\!\!\text{ 100}\] .

Complete step by step answer:
According to the question, a man sells 5 identical articles for Rs. 15 and makes a profit of 20%.
First of all, let us assume that the cost price of one article is Rs. x.
The cost price of one article = Rs. x ………………………………(1)
The cost price of 5 identical articles = Rs. 5x …………………………….(2)
It is given that the man makes a profit of 20% by selling five articles at Rs. 15.
The selling price of 5 articles = Rs. 15 …………………………………..(3)
The profit by selling 5 articles = Rs. 20% of the cost price of 5 articles ………………………………(4)
We know the formula, Selling price = Cost price + profit ………………………….(5)
From equation (2), we have the cost price of five articles and from equation (4), we have the profit by selling 5 articles.
Now, from equation (2), equation (4), and equation (5), we get
\[\begin{align}
  & \Rightarrow Selling\,price=\,5x+\dfrac{20}{100}\times 5x \\
 & \Rightarrow Selling\,price=\,5x\left( 1+\dfrac{20}{100} \right) \\
 & \Rightarrow Selling\,price=\,5x\left( 1+\dfrac{1}{5} \right) \\
 & \Rightarrow Selling\,price=\,5x\left( \dfrac{5+1}{5} \right) \\
 & \Rightarrow Selling\,price=\,5x\left( \dfrac{6}{5} \right) \\
\end{align}\]
\[\Rightarrow Selling\,price=\,6x\] ………………………………(6)
From equation (3), we also have the selling price.
Now, on comparing equation (3) and equation (6), we get
\[\begin{align}
  & \Rightarrow \,6x=15 \\
 & \Rightarrow x=\dfrac{15}{6} \\
 & \Rightarrow x=2.5 \\
\end{align}\]
So, the cost price of one article is Rs. 2.5 ………………………………….(7)
Now, the man is selling 8 articles for Rs. 18.40.
The selling price of 8 articles = Rs. 18.40 ………………………………(8)
From equation (7), we have the cost price of one article.
The cost price of 8 articles = Rs. \[2.5\times 8\] = Rs. 20 …………………………….(9)
We know the formula, Loss = Cost price – selling price …………………………………….(10)
From equation (8), equation (9), and equation (10), we have
\[Loss=Rs.20-Rs.18.40=Rs.1.60\] …………………………………(11)
The percentage of loss can be calculated by using the formula, \[\dfrac{\text{Loss}}{\text{Cost price}}\text{ }\!\!\times\!\!\text{ 100}\] …………………….(12)
Now, from equation (9), equation (11), and equation (12), we have
The percentage of loss = \[\dfrac{Rs.1.60}{Rs.20}\text{ }\!\!\times\!\!\text{ 100=1}\text{.6}\times 5=8\] .
Therefore, the loss percentage after selling 8 articles for Rs. 18.40 is 8%.

Note: In this question, one might make a silly mistake while calculating the loss percentage. One might replace the cost price by Rs. 18.40 in the formula, \[\dfrac{\text{Loss}}{\text{Cost price}}\text{ }\!\!\times\!\!\text{ 100}\] . This is wrong because Rs. 18.40 is the selling price of 8 articles. The cost price of 8 articles is Rs. 20. So, we have to replace the cost price by Rs. 20 in the formula, \[\dfrac{\text{Loss}}{\text{Cost price}}\text{ }\!\!\times\!\!\text{ 100}\] .