Cost price of an article is Rs. 350. If the profit percentage is 35 percent, then what is the value of profit?
Rs. 122.5
Understanding the Profit Calculation Problem
This question asks us to determine the amount of profit earned on an article given its cost price and the profit percentage. We are provided with the cost price (CP) of an article, which is Rs. 350. We are also given that the profit percentage is 35 percent. Our goal is to find the actual value of the profit in rupees.
Key Concepts: Cost Price, Profit Percentage, and Profit
Let's quickly define the terms involved:
- Cost Price (CP): This is the price at which an article is bought. In this case, the cost price is Rs. 350.
- Profit: Profit is the amount gained when an article is sold for more than its cost price.
- Profit Percentage: This is the profit expressed as a percentage of the cost price. The formula for profit percentage is:
\(\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%\)
We can rearrange this formula to find the Profit value:
\(\text{Profit} = \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{Cost Price}\)
Given Information
Let's list the information provided in the question:
| Parameter | Value |
|---|---|
| Cost Price (CP) | Rs. 350 |
| Profit Percentage | 35% |
Calculating the Value of Profit
To find the profit value, we use the rearranged formula mentioned above. We need to calculate 35% of the cost price, which is Rs. 350.
The calculation steps are as follows:
- Identify the Cost Price (CP).
- Identify the Profit Percentage.
- Use the formula: Profit = (Profit Percentage / 100) \(\times\) CP.
Let's apply the values:
\(\text{Profit} = \left(\frac{35}{100}\right) \times 350\)
Now, perform the calculation:
\(\text{Profit} = 0.35 \times 350\)
Multiplying 0.35 by 350:
\(0.35 \times 350 = 122.5\)
So, the value of the profit is Rs. 122.5.
Verification with Options
Let's compare our calculated profit value with the given options:
- Option 1: Rs. 112.8
- Option 2: Rs. 122.5
- Option 3: Rs. 145.6
- Option 4: Rs. 135.6
Our calculated profit of Rs. 122.5 matches Option 2.
Step-by-Step Profit Calculation Summary
- Cost Price (CP) = Rs. 350
- Profit Percentage = 35%
- Profit = 35% of Rs. 350
- Profit = \(\frac{35}{100} \times 350\)
- Profit = \(0.35 \times 350\)
- Profit = Rs. 122.5
Revision Table: Profit & Loss Basics
| Concept | Definition/Formula |
|---|---|
| Cost Price (CP) | Price at which an item is bought. |
| Selling Price (SP) | Price at which an item is sold. |
| Profit | SP - CP (when SP > CP) |
| Loss | CP - SP (when CP > SP) |
| Profit Percentage | \(\left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\%\) |
| Loss Percentage | \(\left(\frac{\text{Loss}}{\text{CP}}\right) \times 100\%\) |
Additional Information: Applications of Profit Percentage
Understanding how to calculate profit percentage and the value of profit is crucial in various real-world scenarios and mathematical problems:
- Business: Businesses use profit calculations to set selling prices, analyze performance, and determine profitability.
- Retail: Retailers calculate profit margins on products to ensure their business is sustainable.
- Finance: Investors might look at profitability metrics of companies.
- Personal Finance: Understanding percentages helps in calculating discounts, interest, and returns on investments.
Profit and loss problems often involve finding the selling price, cost price, profit/loss amount, or profit/loss percentage when other values are known. Always remember that profit and loss percentages are typically calculated with respect to the Cost Price, unless otherwise stated.
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
