Grade 6 Profit - Loss

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Learn about profit and loss through these example problems with detailed step-by-step solutions.

Example 1: Calculating Profit and Profit Percentage

An item is bought for ₹200 and sold for ₹250. Find the profit and profit percentage.

Step 1: Identify cost price (CP) and selling price (SP):

CP = ₹200, SP = ₹250.

Step 2: Calculate profit:

\( \text{Profit} = \text{SP} - \text{CP} = 250 - 200 = 50 \).

Step 3: Calculate profit percentage:

\( \text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{50}{200} \times 100 = 25\% \).

Step 4: Therefore, the profit is ₹50 and the profit percentage is 25%.

Example 2: Calculating Loss and Loss Percentage

An item is bought for ₹300 and sold for ₹270. Find the loss and loss percentage.

Step 1: Identify cost price (CP) and selling price (SP):

CP = ₹300, SP = ₹270.

Step 2: Calculate loss:

\( \text{Loss} = \text{CP} - \text{SP} = 300 - 270 = 30 \).

Step 3: Calculate loss percentage:

\( \text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100 = \frac{30}{300} \times 100 = 10\% \).

Step 4: Therefore, the loss is ₹30 and the loss percentage is 10%.

Example 3: Finding Selling Price with Profit Percentage

An item has a cost price of ₹400 and a profit of 20%. Find the selling price.

Step 1: Identify cost price (CP) and profit percentage:

CP = ₹400, Profit = 20%.

Step 2: Calculate profit:

\( \text{Profit} = \frac{20}{100} \times 400 = 80 \).

Step 3: Calculate selling price:

\( \text{SP} = \text{CP} + \text{Profit} = 400 + 80 = 480 \).

Step 4: Alternative method:

\( \text{SP} = \text{CP} \times (1 + \frac{\text{Profit \%}}{100}) = 400 \times (1 + 0.2) = 400 \times 1.2 = 480 \).

Step 5: Therefore, the selling price is ₹480.

Example 4: Finding Cost Price with Loss Percentage

An item is sold for ₹180 with a loss of 10%. Find the cost price.

Step 1: Identify selling price (SP) and loss percentage:

SP = ₹180, Loss = 10%.

Step 2: Let cost price (CP) be \( x \). Since loss is 10%:

\( \text{SP} = \text{CP} \times (1 - \frac{\text{Loss \%}}{100}) \).

\( 180 = x \times (1 - 0.1) = x \times 0.9 \).

Step 3: Solve for \( x \):

\( x = \frac{180}{0.9} = 200 \).

Step 4: Verify:

Loss = \( 10\% \text{ of } 200 = 20 \), SP = \( 200 - 20 = 180 \), which matches.

Step 5: Therefore, the cost price is ₹200.

Example 5: Real-World Profit Problem

A shopkeeper buys an item for ₹500 and wants a 15% profit. Find the selling price.

Step 1: Identify cost price (CP) and profit percentage:

CP = ₹500, Profit = 15%.

Step 2: Calculate profit:

\( \text{Profit} = \frac{15}{100} \times 500 = 75 \).

Step 3: Calculate selling price:

\( \text{SP} = \text{CP} + \text{Profit} = 500 + 75 = 575 \).

Step 4: Alternative method:

\( \text{SP} = \text{CP} \times (1 + \frac{\text{Profit \%}}{100}) = 500 \times (1 + 0.15) = 500 \times 1.15 = 575 \).

Step 5: Therefore, the selling price is ₹575.

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Note: This solver handles calculating profit/loss and percentage (e.g., Cost price ₹100, selling price ₹120; find profit and percentage), finding selling price (e.g., Cost price ₹200, profit 10%; find selling price), finding cost price (e.g., Selling price ₹150, loss 25%; find cost price), and real-world problems (e.g., Buy for ₹400, want 20% profit; find selling price). Enter the problem clearly.

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Use formats like 'Cost price ₹100, selling price ₹120; find profit and percentage', 'Cost price ₹200, profit 10%; find selling price', 'Selling price ₹150, loss 25%; find cost price', or 'Buy for ₹400, want 20% profit; find selling price'.