A trader sells an article at 20 percent profit. If he buys it at half of the cost price and sells at the same selling price as before, then what will be the profit percentage?
140 percent
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.
| Item | Scenario 1 (Original) | Scenario 2 (New) |
|---|---|---|
| Cost Price (CP) | Rs. 100 (assumed) | Rs. 50 (Half of Original CP) |
| Profit % | 20% | Calculated (140%) |
| Selling Price (SP) | Rs. 120 (CP + 20% profit) | Rs. 120 (Same as Scenario 1 SP) |
| Profit Amount | Rs. 20 | Rs. 70 (SP - CP) |
Revision Table
| Concept | Formula | Notes |
|---|---|---|
| Profit | Selling Price - Cost Price (when SP > CP) | Indicates gain from a transaction. |
| Profit Percentage | $\frac{\text{Profit}}{\text{Cost Price}} \times 100\%$ | Always calculated on the Cost Price. |
| Selling Price with Profit | $\text{CP} \times (1 + \frac{\text{Profit \%}}{100})$ | A quick way to find SP if profit % is known. |
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.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
