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
Calculating Profit Percentage in a Trader Scenario
This problem involves calculating the profit percentage under changed conditions, specifically when the cost price is reduced while the selling price remains the same. We can solve this by considering two scenarios.
Let's assume an initial cost price to make the calculations easy. A common practice is to assume the cost price is ₹100.
Scenario 1: Original Trading Conditions
The trader sells an article at a 20 percent profit.
Let the original Cost Price ($\text{CP}_1$) be ₹100.
The profit is 20% of the Cost Price.
Profit = $20\%$ of $\text{CP}_1 = \frac{20}{100} \times 100 = \text{₹}20$.
The original Selling Price ($\text{SP}_1$) is the Cost Price plus the Profit.
$\text{SP}_1 = \text{CP}_1 + \text{Profit} = 100 + 20 = \text{₹}120$.
Scenario 2: Changed Trading Conditions
The trader buys the article at half of the original cost price.
The new Cost Price ($\text{CP}_2$) is half of $\text{CP}_1$.
$\text{CP}_2 = \frac{1}{2} \times \text{CP}_1 = \frac{1}{2} \times 100 = \text{₹}50$.
The trader sells the article at the same selling price as before. This means the new selling price is the same as the original selling price.
The new Selling Price ($\text{SP}_2$) = $\text{SP}_1 = \text{₹}120$.
Calculating the New Profit Percentage
In Scenario 2, the trader's profit is the difference between the new selling price and the new cost price.
Profit = $\text{SP}_2 - \text{CP}_2 = 120 - 50 = \text{₹}70$.
The profit percentage is always calculated based on the cost price. In this case, it is calculated on the new cost price ($\text{CP}_2$).
Profit Percentage = $\left( \frac{\text{Profit}}{\text{CP}_2} \right) \times 100\%$.
Substituting the values we found for Scenario 2:
Profit Percentage = $\left( \frac{70}{50} \right) \times 100\%$.
Profit Percentage = $\left( \frac{7}{5} \right) \times 100\%$.
Profit Percentage = $1.4 \times 100\% = 140\%$.
Thus, the profit percentage in the second scenario is 140 percent.
Summary of Scenarios
| Item | Scenario 1 (Original) | Scenario 2 (Changed) |
|---|---|---|
| Cost Price (CP) | ₹100 (Assumed) | ₹50 (Half of ₹100) |
| Selling Price (SP) | ₹120 (₹100 + 20% Profit) | ₹120 (Same as Scenario 1) |
| Profit | ₹20 (₹120 - ₹100) | ₹70 (₹120 - ₹50) |
| Profit Percentage | 20% $\left( \frac{20}{100} \times 100\% \right)$ | 140% $\left( \frac{70}{50} \times 100\% \right)$ |
Revision Table: Important Profit & Loss Terms
| Term | Definition/Formula | Notes |
|---|---|---|
| Cost Price (CP) | Price at which goods are bought. | Basis for calculating profit/loss percentage. |
| Selling Price (SP) | Price at which goods are sold. | Determines if there is a profit or loss. |
| Profit | SP - CP (when SP > CP) | The gain from a transaction. |
| Loss | CP - SP (when CP > SP) | The loss incurred in a transaction. |
| Profit Percentage | $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%$ | Profit as a percentage of CP. |
| Loss Percentage | $\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%$ | Loss as a percentage of CP. |
Additional Information: Understanding Percentage Concepts
Percentage is a way of expressing a part of a whole in terms of 100. Profit percentage indicates how much profit is made for every 100 units of cost price.
- A 20% profit means the selling price is 120% of the cost price.
- When the cost price is halved, and the selling price remains the same, the profit amount increases relative to the new, lower cost price.
- Calculating percentages correctly requires identifying the base value, which is the cost price in profit/loss percentage calculations.
These percentage calculations are crucial for understanding financial performance and are frequently tested in various exams.
Important Questions from Dishonest Dealings
A shopkeeper uses a weight of 460 grams instead of 500 grams and sells the articles at their cost price, what is his profit percentage?
A dishonest shopkeeper sells sugar at a rate of Rs. 45 per kg. The cost price of the sugar is Rs. 40 per kg. Even after doing this, he tries to increase his profit by removing 100 gm from each packet of 1 kg. What is the gain percent of the shopkeeper?
A dishonest dealer sells the goods at 7% loss on cost price but uses 18% less weight. What is his percentage of profit? (Correct to 2 decimal places)
A shopkeeper cheats to the extent of 11% while buying and selling fruits, by using tampered weights. His total gain in percentage is.
A. 23.25
B. 23.21
C. 24.71
C. 23.5
A dishonest shopkeeper claimed to have sold an item at ₹23/kg, which cost him ₹25/kg. However, by using faulty weights, he gave only 600 grams instead of 1 kg. What is his total percentage profit or loss?
