Solving the Profit Percentage Problem

This problem involves calculating the profit percentage for a trader under two different scenarios related to the cost price and selling price of an article. Let's break it down.

Understanding the Two Scenarios

We are given information about a trader selling an article. There are two distinct situations described:

• Scenario 1: The trader sells the article at a 20 percent profit on the original cost price.
• Scenario 2: The trader buys the same article at half of the original cost price and sells it at the same selling price as in Scenario 1. We need to find the profit percentage in this scenario.

Step-by-Step Calculation of Profit Percentage

To make the calculation clear, let's assume a value for the original cost price (CP).

• Let the original Cost Price (CP1) of the article be Rs. 100.
• In Scenario 1, the trader makes a 20 percent profit.
• Profit in Scenario 1 = 20% of CP1 = $\frac{20}{100} \times 100 = 20$ Rupees.
• The Selling Price in Scenario 1 (SP1) = CP1 + Profit = Rs. 100 + Rs. 20 = Rs. 120.

Now, let's consider Scenario 2:

• The trader buys the article at half of the original cost price.
• New Cost Price (CP2) = $\frac{1}{2} \times$ Original CP1 = $\frac{1}{2} \times 100 = 50$ Rupees.
• The trader sells the article at the same selling price as before.
• Selling Price in Scenario 2 (SP2) = SP1 = Rs. 120.

Now, we need to find the profit percentage in Scenario 2.

• Profit in Scenario 2 = SP2 - CP2 = Rs. 120 - Rs. 50 = Rs. 70.
• Profit percentage is calculated based on the cost price in that scenario (CP2).
• Profit Percentage in Scenario 2 = $\frac{\text{Profit}}{\text{CP2}} \times 100\%$
• Profit Percentage in Scenario 2 = $\frac{70}{50} \times 100\%$
• Profit Percentage in Scenario 2 = $\frac{7}{5} \times 100\%$
• Profit Percentage in Scenario 2 = $7 \times 20\%$
• Profit Percentage in Scenario 2 = $140\%$

So, if the trader buys the article at half the original cost price and sells at the same selling price, the profit percentage will be 140 percent.

Revision Table

Additional Information on Profit and Loss Calculations

Profit and loss concepts are fundamental in business and quantitative aptitude. Understanding how changes in cost price or selling price affect profit percentage is crucial.

• Cost Price (CP): The price at which an article is bought.
• Selling Price (SP): The price at which an article is sold.
• Profit: Occurs when SP > CP. Profit = SP - CP.
• Loss: Occurs when CP > SP. Loss = CP - SP.
• Loss Percentage: $\frac{\text{Loss}}{\text{Cost Price}} \times 100\%$. Always calculated on the Cost Price.

When solving problems like this, assuming a base value (like 100 or any other number) for the cost price often simplifies the calculations and makes the logic easier to follow, as the profit percentage is independent of the absolute value of the cost price or selling price, depending only on their ratio.