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Every day, we buy and sell goods or services. Whether you are shopping at a market, running a business, or even participating in a competitive exam, understanding how profit and loss work is essential. Profit and loss help us understand whether we are gaining or losing money in a transaction.
In this section, we will learn about the key terms like cost price and selling price, and how to calculate profit and loss. These concepts are closely related to percentages and basic arithmetic, which you have already studied. By mastering profit and loss, you will be able to solve many practical problems and perform well in exams.
Let's start by defining the important terms:
Understanding these terms is the first step to solving profit and loss problems.
Note: If the selling price is less than the cost price, the profit area disappears, and instead, the loss area appears to the left of CP.
Profit and loss are often expressed as percentages to understand the gain or loss relative to the cost price. This helps compare profits or losses across different transactions easily.
Here are the essential formulas you will use to solve profit and loss problems:
| Formula Name | Formula | Variables |
|---|---|---|
| Profit | \( \text{Profit} = SP - CP \) | SP = Selling Price, CP = Cost Price |
| Loss | \( \text{Loss} = CP - SP \) | CP = Cost Price, SP = Selling Price |
| Profit Percentage | \( \text{Profit \%} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \) | Profit = SP - CP, CP = Cost Price |
| Loss Percentage | \( \text{Loss \%} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \) | Loss = CP - SP, CP = Cost Price |
| Selling Price from Profit % | \( SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \) | CP = Cost Price, Profit % = Profit Percentage |
| Selling Price from Loss % | \( SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \) | CP = Cost Price, Loss % = Loss Percentage |
| Cost Price from SP and Profit % | \( CP = \frac{SP}{1 + \frac{\text{Profit \%}}{100}} \) | SP = Selling Price, Profit % = Profit Percentage |
| Cost Price from SP and Loss % | \( CP = \frac{SP}{1 - \frac{\text{Loss \%}}{100}} \) | SP = Selling Price, Loss % = Loss Percentage |
Step 1: Calculate the profit using the formula:
\( \text{Profit} = SP - CP = 600 - 500 = Rs.100 \)
Step 2: Calculate the profit percentage:
\( \text{Profit \%} = \left( \frac{100}{500} \right) \times 100 = 20\% \)
Answer: Profit is Rs.100 and profit percentage is 20%.
Step 1: Use the formula for selling price when loss percentage is given:
\( SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \)
Step 2: Substitute the values:
\( SP = 1200 \times \left(1 - \frac{10}{100}\right) = 1200 \times 0.9 = Rs.1080 \)
Answer: The selling price is Rs.1080.
Step 1: Calculate the price after the first discount of 10%:
\( \text{Price after 1st discount} = 2000 \times (1 - 0.10) = 2000 \times 0.90 = Rs.1800 \)
Step 2: Calculate the price after the second discount of 5% on Rs.1800:
\( \text{Price after 2nd discount} = 1800 \times (1 - 0.05) = 1800 \times 0.95 = Rs.1710 \)
Step 3: This final price is the selling price (SP). Now calculate profit or loss:
\( \text{Profit} = SP - CP = 1710 - 1600 = Rs.110 \)
Step 4: Since profit is positive, calculate profit percentage:
\( \text{Profit \%} = \left( \frac{110}{1600} \right) \times 100 = 6.875\% \)
Answer: Profit is Rs.110, which is approximately 6.88%.
graph TD A[Marked Price = Rs.2000] --> B[Apply 10% discount] B --> C[Price = Rs.1800] C --> D[Apply 5% discount] D --> E[Final SP = Rs.1710] E --> F[Compare with CP = Rs.1600] F --> G[Profit = Rs.110] G --> H[Profit % = 6.88%]
Step 1: Use the formula for cost price when selling price and profit percentage are given:
\( CP = \frac{SP}{1 + \frac{\text{Profit \%}}{100}} \)
Step 2: Substitute the values:
\( CP = \frac{1320}{1 + \frac{10}{100}} = \frac{1320}{1.10} = Rs.1200 \)
Answer: The cost price is Rs.1200.
Step 1: Calculate the profit:
\( \text{Profit} = SP - CP = 880 - 800 = Rs.80 \)
Step 2: Calculate the profit percentage:
\( \text{Profit \%} = \left( \frac{80}{800} \right) \times 100 = 10\% \)
Answer: Profit percentage is 10%.
When to use: When cost price and profit or loss percentage are known, and you need to find selling price fast.
When to use: To avoid confusion and errors during percentage calculations.
When to use: When solving problems with multiple successive discounts.
When to use: During mental math or quick calculations.
When to use: In time-limited exams requiring quick answers.
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