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:

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:

1. Identify the Cost Price (CP).
2. Identify the Profit Percentage.
3. 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

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.