Understanding the Articles Purchase and Loss Problem

The question asks us to find the selling price of a single article given the total cost price of a batch of articles and a specific condition about the loss incurred during the sale.

We are given that Ramesh purchases 75 articles for a total cost of ₹ 10800. This is the cost price (CP) for 75 articles.

The selling condition states that he sells these 75 articles at a loss equal to the selling price of 5 articles. We need to determine the selling price (SP) of one article.

Setting up the Calculation for Selling Price

Let's denote the selling price of one article as \(SP\). The total selling price for 75 articles will be \(75 \times SP\).

The loss incurred is given as the selling price of 5 articles. So, the total loss is \(5 \times SP\).

The fundamental relationship between Cost Price, Selling Price, and Loss is:

\(\text{Loss} = \text{Cost Price} - \text{Selling Price}\)

In this case, this applies to the total transaction involving 75 articles:

\(\text{Loss on 75 articles} = \text{CP of 75 articles} - \text{SP of 75 articles}\)

Formulating the Equation

Now, let's substitute the given values and expressions into the loss equation:

• Loss on 75 articles = \(5 \times SP\)
• CP of 75 articles = ₹ 10800
• SP of 75 articles = \(75 \times SP\)

So, the equation becomes:

\(5 \times SP = 10800 - (75 \times SP)\)

Solving for the Selling Price of One Article

We now need to solve this linear equation for \(SP\):

\(5SP = 10800 - 75SP\)

To isolate the term with \(SP\), we add \(75SP\) to both sides of the equation:

\(5SP + 75SP = 10800\)

\(80SP = 10800\)

Now, to find the value of \(SP\), divide both sides by 80:

\(SP = \frac{10800}{80}\)

\(SP = \frac{1080}{8}\)

Performing the division:

\(1080 \div 8 = 135\)

So, the selling price of one article is ₹ 135.

Verifying the Result

Let's check if this selling price satisfies the condition. SP of one article = ₹ 135

• SP of 75 articles = \(75 \times 135\) = ₹ 10125
• CP of 75 articles = ₹ 10800
• Loss = CP - SP = \(10800 - 10125\) = ₹ 675

The loss is stated to be equal to the selling price of 5 articles.

• SP of 5 articles = \(5 \times 135\) = ₹ 675

Since the calculated loss (₹ 675) is equal to the selling price of 5 articles (₹ 675), our calculated selling price of ₹ 135 per article is correct.

Summary of the Calculation Steps

Revision Table: Profit and Loss Concepts

Additional Information: Solving Word Problems

Solving word problems like this one often involves translating the given information into mathematical equations. Here are some tips:

• Read Carefully: Understand what is given and what needs to be found.
• Identify Variables: Assign variables (like \(SP\), \(CP\), Loss) to the unknown quantities.
• Formulate Equations: Use the relationships between the variables (like Loss = CP - SP) to write equations based on the problem description.
• Solve Equations: Use algebraic techniques to solve for the unknown variable(s).
• Check Your Answer: Substitute the calculated value back into the original problem or equation to ensure it makes sense and satisfies all conditions.

In this problem, recognizing that the loss was given in terms of the selling price of a certain number of articles was key to setting up the correct equation.