Understanding Loss Percentage: When the Cost Price of 8 Pencils Equals the Selling Price of 10 Pencils

Have you ever wondered what would happen if the cost price of 8 pencils is equivalent to the selling price of 10 pencils? This intriguing scenario introduces us to the concept of loss percentage. In this article, we will delve into the process of calculating the loss percentage under such circumstances.

Introduction to Cost Price and Selling Price

The cost price (CP) of a pencil is the price at which goods are purchased, while the selling price (SP) is the price at which goods are sold. In some economic scenarios, the relationship between these two prices might not be straightforward. For instance, in the given scenario, the cost price of 8 pencils is equal to the selling price of 10 pencils. This article will explain how to calculate the loss percentage in such a situation.

Calculating Loss Percentage

Let the cost price (CP) of one pencil be x. Therefore, the cost price of 8 pencils is 8x. Let the selling price (SP) of one pencil be y. Therefore, the selling price of 10 pencils is 10y.

According to the given problem, the cost price of 8 pencils is equal to the selling price of 10 pencils:

8x 10y

We can express y in terms of x:

y (frac{8x}{10}) (frac{4x}{5})

Next, we calculate the loss per pencil:

Loss CP - SP x - (frac{4x}{5}) (frac{x - 4x}{5}) (frac{x}{5})

Now, we calculate the loss percent using the formula:

Loss Percent (left(frac{frac{x}{5}}{x}right) times 100 frac{1}{5} times 100 20)

Therefore, the loss percent is 20%. This means that for each pencil, there is a 20% loss compared to the cost price.

Real-World Example

Let us consider a real-world example to further illustrate this concept. Suppose the cost price of 8 pencils is Rs 40. Therefore, the cost price per pencil is Rs 5. The selling price of 10 pencils is also Rs 40. Consequently, the selling price per pencil is Rs 4. The loss per pencil is Rs 1 (Rs 5 - Rs 4). The loss percentage can be calculated as follows:

Loss Percent (frac{1 times 100}{5} 20%)

Another example: If the selling price of 10 articles is Rs x, then the selling price of 1 article is Rs (frac{x}{10}). If the cost price of 8 articles is Rs x, then the cost price of 1 article is Rs (frac{x}{8}). The cost price of 1 article is greater than the selling price of 1 article.

Loss CP - SP Rs (frac{x}{8}) - Rs (frac{x}{10}) Rs (frac{x}{40})

Percent Loss (frac{Loss}{CP} times 100 frac{frac{x}{40}}{frac{x}{8}} times 100 20%)

Hence, the required loss percentage is 20%.

Conclusion

In the scenario where the cost price of 8 pencils equals the selling price of 10 pencils, the loss percentage can be calculated to be 20%. Understanding such scenarios is crucial for businesses and individuals to make informed decisions about pricing strategies and inventory management.

Key Takeaways:

Cost price and selling price play a vital role in calculating the loss percentage. The formula for calculating loss percentage is: Loss Percent (left(frac{CP - SP}{CP}right) times 100). Through examples, we have demonstrated how to calculate loss percentage under various economic scenarios.