Comprehensive Study Guide on Profit, Loss, Percentage Calculations, and Unit Price

Fundamental Financial Formulas

• Definitions of Primary Variables:

  • Cost Price ($CP$): The total initial amount paid to purchase an item or quantity of goods.

  • Selling Price ($SP$): The total amount of money received when an item or quantity of goods is sold.

  • Profit: The positive financial gain realized when the selling price exceeds the cost price ($SP > CP$).

  • Loss: The financial decrease incurred when the cost price exceeds the selling price ($CP > SP$).

  • Unit Price: The cost attributed to a single item when goods are purchased as a group or in bulk.

• Core Governing Equations:

  • Profit Formula:     $\text{Profit} = SP - CP$

  • Loss Formula:     $\text{Loss} = CP - SP$

  • Selling Price Relationship with Loss:     $SP = CP - \text{Loss}$

  • Profit Percentage Formula:     $\text{Profit Percentage} = \frac{\text{Profit}}{CP} \times 100\%$

  • Loss Percentage Formula:     $\text{Loss Percentage} = \frac{\text{Loss}}{CP} \times 100\%$

  • Monetary Loss from Loss Percentage:     $\text{Loss} = \frac{\text{Loss Percentage}}{100} \times CP$

  • Unit Price Formula:     $\text{Unit Price} = \frac{\text{Total Cost Price}}{\text{Number of items}}$

Absolute Profit and Loss Calculations

• Direct Loss Calculation:

  • Given Values:

  • Cost Price ($CP$) = \\n$850

  • Selling Price ($SP$) = \\n$765

  • Method:

  • Apply the absolute loss formula:       $\text{Loss} = CP - SP$

  • Substitute given numerical quantities:       $\text{Loss} = \\n$850 - \\n$765$

  • Result:

  • Absolute Loss = \\n$85

• Direct Profit Calculation:

  • Given Values:

  • Cost Price ($CP$) = \\n$40

  • Selling Price ($SP$) = \\n$72

  • Method:

  • Apply the absolute profit formula:       $\text{Profit} = SP - CP$

  • Substitute given numerical quantities:       $\text{Profit} = \\n$72 - \\n$40$

  • Result:

  • Absolute Profit = \\n$32

Profit Percentage Calculations

• Calculating Profit Rate from Financial Transactions:

  • Given Values:

  • Cost Price ($CP$) = \\n$200

  • Selling Price ($SP$) = \\n$250

  • Step-by-Step Procedure:

  • Step 1: Determine absolute profit:       $\text{Profit} = SP - CP$       $\text{Profit} = \\n$250 - \\n200 = \\n$50

  • Step 2: Formulate the percentage equation relative to the cost price:       $\text{Profit Percentage} = \frac{\text{Profit}}{CP} \times 100\%$       $\text{Profit Percentage} = \frac{50}{200} \times 100\%$

  • Step 3: Reduce fraction and evaluate arithmetic:       $\frac{50}{200} = \frac{1}{4}$       $\text{Profit Percentage} = \frac{1}{4} \times 100\% = 25\%$

  • Alternative Working Method:       $\frac{50 \times 100}{200} = \frac{5000}{200} = 25\%$

Loss Percentage Calculations

• Calculating Loss Rate from Financial Transactions:

  • Given Values:

  • Cost Price ($CP$) = \\n$160

  • Selling Price ($SP$) = \\n$136

  • Step-by-Step Procedure:

  • Step 1: Determine absolute monetary loss:       $\text{Loss} = CP - SP$       $\text{Loss} = \\n$160 - \\n136 = \\n$24

  • Step 2: Formulate the percentage equation relative to the cost price:       $\text{Loss Percentage} = \frac{\text{Loss}}{CP} \times 100\%$       $\text{Loss Percentage} = \frac{24}{160} \times 100\%$

  • Step 3: Evaluate arithmetic:       $\frac{24 \times 100}{160} = \frac{2400}{160} = 15\%$

  • Result:

  • Loss Percentage = $15\%$

Determining Selling Price and Loss from Percentage Loss

• Calculating Monetary Loss and Final Selling Price:

  • Given Values:

  • Cost Price ($CP$) = \\n$1500

  • Loss Percentage = $12\%$

  • Step-by-Step Procedure:

  • Step 1: Compute absolute monetary loss:       \text{Loss} = \frac{12}{100} \times \\n$1500       \text{Loss} = 12 \times 15 = \\n$180

  • Step 2: Compute final selling price ($SP$):       $SP = CP - \text{Loss}$       $SP = \\n$1500 - \\n180 = \\n$1320

  • Final Results:

  • Loss = \\n$180

  • Selling Price ($SP$) = \\n$1320

Unit Price Calculations

• Calculating Individual Item Cost:

  • Given Values:

  • Total Cost Price ($CP$) for bulk exercise books = \\n$52.00

  • Total number of exercise books = $8$

  • Step-by-Step Procedure:

  • Step 1: Apply unit price ratio:       $\text{Unit Price} = \frac{\text{Total Cost Price}}{\text{Number of items}}$

  • Step 2: Substitute values:       \text{Unit Price} = \frac{\\n$52.00}{8}

  • Step 3: Perform division:       $52 \div 8 = 6.50$

  • Final Answer:

  • Cost of one exercise book = \\n$6.50

Fundamental Financial Formulas

• Definitions of Primary Variables:

  • Cost Price ($CP$): The total initial amount paid to purchase an item.

  • Selling Price ($SP$): The total amount received when an item is sold.

  • Profit: Money gained when selling price is greater than cost price ($SP > CP$).

  • Loss: Money lost when cost price is greater than selling price ($CP > SP$).

  • Unit Price: Cost of a single item when bought in bulk.

• Core Governing Equations (Simplified):

  • Profit: $<br>\text{Profit} = SP - CP<br>$

  • Loss: $<br>\text{Loss} = CP - SP<br>$

  • Selling Price (with Loss): $<br>SP = CP - \text{Loss}<br>$

  • Profit Percentage: $<br>\text{Profit } \% = \frac{\text{Profit}}{CP} \times 100\%<br>$

  • Loss Percentage: $<br>\text{Loss } \% = \frac{\text{Loss}}{CP} \times 100\%<br>$

  • Monetary Loss: $<br>\text{Loss} = \frac{\text{Loss } \%}{100} \times CP<br>$

  • Unit Price: $<br>\text{Unit Price} = \frac{\text{Total } CP}{\text{Number of Items}}<br>$

Absolute Profit and Loss Calculations

• Direct Loss Calculation:

  • Given: $CP = \$850$, $SP = \$765$

  • Formula: $<br>\text{Loss} = CP - SP<br>$

  • Calculation: $<br>\text{Loss} = \$850 - \$765 = \$85<br>$

• Direct Profit Calculation:

  • Given: $CP = \$40$, $SP = \$72$

  • Formula: $<br>\text{Profit} = SP - CP<br>$

  • Calculation: $<br>\text{Profit} = \$72 - \$40 = \$32<br>$

Profit Percentage Calculations

• Calculating Profit Rate:

  • Given: $CP = \$200$, $SP = \$250$

  • Step 1: Find Profit: $<br>\text{Profit} = \$250 - \$200 = \$50<br>$

  • Step 2: Calculate Percentage: $<br>\text{Profit } \% = \frac{\$50}{\$200} \times 100\% = 25\%<br>$

Loss Percentage Calculations

• Calculating Loss Rate:

  • Given: $CP = \$160$, $SP = \$136$

  • Step 1: Find Loss: $<br>\text{Loss} = \$160 - \$136 = \$24<br>$

  • Step 2: Calculate Percentage: $<br>\text{Loss } \% = \frac{\$24}{\$160} \times 100\% = 15\%<br>$

Determining Selling Price and Loss from Percentage Loss

• Calculating Monetary Loss and Selling Price:

  • Given: $CP = \$1500$, $\text{Loss } \% = 12\%$

  • Step 1: Find Loss Amount: $<br>\text{Loss} = \frac{12}{100} \times \$1500 = \$180<br>$

  • Step 2: Find Selling Price: $<br>SP = \$1500 - \$180 = \$1320<br>$

Unit Price Calculations

• Calculating Individual Item Cost:

  • Given: $\text{Total } CP = \$52.00$ for $8$ items

  • Formula: $<br>\text{Unit Price} = \frac{\text{Total } CP}{\text{Number of Items}}<br>$

  • Calculation: $$
    \text{Unit Price} = \frac{\$52.00}{8} = \$6