Understanding the Profit and Loss Problem

This question asks us to find the original cost price of a laptop given its selling price and the percentage of profit earned. Understanding the relationship between cost price (CP), selling price (SP), and profit percentage is key to solving this problem.

Key Information Provided

• Selling Price (SP) of the laptop = Rs. 55,000
• Profit Percentage = 25%

Finding the Cost Price (CP)

When a profit is made, the selling price is the cost price plus the profit amount. The profit percentage is calculated on the cost price.

We can express the selling price in terms of the cost price and the profit percentage using the formula:

$$ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) $$

Alternatively, we can think of the selling price as representing the original cost price (100%) plus the profit percentage. So, if there is a 25% profit, the selling price is 100% + 25% = 125% of the cost price.

Let's use the formula to find the cost price (CP):

Given:

• SP = 55,000
• Profit Percentage = 25

Substitute the values into the formula:

$$ 55,000 = \text{CP} \times \left(1 + \frac{25}{100}\right) $$

Simplify the term in the parenthesis:

$$ 1 + \frac{25}{100} = 1 + 0.25 = 1.25 $$

So, the equation becomes:

$$ 55,000 = \text{CP} \times 1.25 $$

To find CP, divide the selling price by 1.25:

$$ \text{CP} = \frac{55,000}{1.25} $$

Performing the division:

$$ \text{CP} = 44,000 $$

So, the cost price of the laptop is Rs. 44,000.

Step-by-Step Cost Price Calculation

1. Identify the Selling Price (SP) and Profit Percentage.
2. Understand that SP = CP + Profit.
3. Understand that Profit Percentage = (Profit / CP) × 100.
4. Recognize that SP represents (100% + Profit %) of CP.
5. Set up the equation: SP = CP × (1 + Profit % / 100).
6. Substitute the given values: 55,000 = CP × (1 + 25/100).
7. Simplify: 55,000 = CP × 1.25.
8. Solve for CP: CP = 55,000 / 1.25.
9. Calculate the result: CP = 44,000.

The cost price of the laptop is Rs. 44,000.

Checking the Answer

Let's verify if selling at Rs. 55,000 on a CP of Rs. 44,000 gives a 25% profit.

Profit = SP - CP = 55,000 - 44,000 = Rs. 11,000

Profit Percentage = $$ \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{11,000}{44,000}\right) \times 100 $$

$$ \left(\frac{11}{44}\right) \times 100 = \left(\frac{1}{4}\right) \times 100 = 0.25 \times 100 = 25\% $$

This matches the given profit percentage, confirming that the calculated cost price is correct.

Revision Table: Profit and Loss Formulas

Additional Information on Profit and Loss

Profit and loss are fundamental concepts in business and finance, used to determine the financial outcome of a transaction. They are always calculated with respect to the cost price unless otherwise specified.

• Cost Price (CP): The original price at which an item is bought.
• Selling Price (SP): The price at which an item is sold.
• Profit: Occurs when SP > CP. It is the gain made on selling an item.
• Loss: Occurs when CP > SP. It is the deficit incurred on selling an item.
• Percentage Calculation: Profit percentage and loss percentage provide a standardized way to compare the profitability or loss across different items, irrespective of their absolute prices.

These concepts are crucial for understanding pricing, calculating margins, and evaluating the performance of sales activities.