Calculating Profit Percentage: Buy Low, Sell High

This question asks us to determine the profit or loss percentage when an article is purchased at a certain percentage less than its value and sold at a certain percentage more than its value.

Understanding the Problem Setup

Let's assume a 'value' for the article. This value serves as a reference point for both the purchase price and the selling price. Since the percentages are given, we can assume any value for the article, and the final profit percentage will remain the same. Let's assume the value of the article is 100 units.

• Value of the Article: \(V = 100\)

Step-by-Step Profit Calculation

Now, let's calculate the cost price (CP) and the selling price (SP) based on the information given:

• Cost Price (CP): The man buys the article for 10 percent less than its value.
  • Discount amount = 10% of Value = \(0.10 \times V\)
  • CP = Value - Discount amount = \(V - 0.10V = 0.90V\)
  • Substituting \(V=100\), CP = \(0.90 \times 100 = 90\)
• Selling Price (SP): The man sells the article for 10 percent more than its value.
  • Premium amount = 10% of Value = \(0.10 \times V\)
  • SP = Value + Premium amount = \(V + 0.10V = 1.10V\)
  • Substituting \(V=100\), SP = \(1.10 \times 100 = 110\)

Since the selling price (SP = 110) is greater than the cost price (CP = 90), there is a profit.

• Profit: Profit = SP - CP
  • Profit = \(110 - 90 = 20\)

Now, we need to calculate the profit percentage. The profit percentage is always calculated on the cost price.

• Profit Percentage: Profit percentage = \(\left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\)
  • Profit Percentage = \(\left(\frac{20}{90}\right) \times 100\)
  • Profit Percentage = \(\left(\frac{2}{9}\right) \times 100\)
  • Profit Percentage = \(\frac{200}{9}\) percent

Let's convert the fraction \(\frac{200}{9}\) into a decimal:

\(\frac{200}{9} = 22.222...\)

So, the profit percentage is approximately 22.2 percent.

This calculation shows a profit of approximately 22.2 percent.

Profit & Loss Revision Table

Additional Information on Profit and Loss Concepts

In profit and loss problems, it is crucial to identify whether the percentage is based on the cost price, selling price, or in this case, an external 'value'. Unless specified otherwise, profit or loss percentage is always calculated on the Cost Price (CP).

In this specific problem, the CP was 10% less than the value, and SP was 10% more than the value. The key was to first find the CP and SP based on the assumed value and then calculate the profit percentage using the standard formula relative to the CP.

Understanding the difference between profit/loss calculated on CP versus SP is important. If a question asks for profit/loss percentage on SP, the denominator in the formula changes.

Many problems can be simplified by assuming a base value like 100, which makes percentage calculations straightforward.