Key Concepts:
Cost Price (CP):
The original price at which an item is purchased.Selling Price (SP):
The price at which an item is sold.Profit:
The gain obtained when an item is sold for more than its cost price. \[ \text{Profit} = \text{SP} - \text{CP} \]Loss:
The amount lost when an item is sold for less than its cost price. \[ \text{Loss} = \text{CP} - \text{SP} \]Profit Percentage:
\[ \text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]Loss Percentage:
\[ \text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]Discount:
A reduction in the marked price of an item. \[ \text{Discount} = \text{Marked Price} - \text{Selling Price} \]Discount Percentage:
\[ \text{Discount \%} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 \]Markup:
The percentage increase on the cost price before selling. \[ \text{Selling Price} = \text{Cost Price} + \left( \frac{\text{Markup \%} \times \text{CP}}{100} \right) \]Examples:
Example 1: Finding Profit Percentage
A trader buys a shirt for \\(40 and sells it for \\)50. Find the profit percentage.Solution:
Step 1: Compute the profit. \[ \text{Profit} = 50 - 40 = 10. \] Step 2: Compute the profit percentage. \[ \text{Profit \%} = \left( \frac{10}{40} \right) \times 100 = 25\%. \] Thus, the profit percentage is **25\%**.Example 2: Finding Discount Percentage
A store sells a bicycle originally marked at \\(200 for \\)170 after applying a discount. Find the discount percentage.Solution:
Step 1: Compute the discount. \[ \text{Discount} = 200 - 170 = 30. \] Step 2: Compute the discount percentage. \[ \text{Discount \%} = \left( \frac{30}{200} \right) \times 100 = 15\%. \] Thus, the discount percentage is **15\%**.Example 3: Calculating Actual Percentage Profit
A television set was marked for sale at N760.00 in order to make a profit of 20\%. The television set was actually sold at a discount of 5\%. Calculate, correct to 2 significant figures, the actual percentage profit.Solution:
Step 1: Find the cost price (CP). Since the marked price includes a 20\% profit on the cost price, we set up the equation: \[ \text{Marked Price} = \text{CP} + 20\% \times \text{CP} = 1.2 \times \text{CP} \] Given the marked price is N760: \[ \text{CP} = \frac{760}{1.2} = 633.33 \] Step 2: Find the actual selling price (SP). Since a 5\% discount is applied: \[ \text{SP} = \text{Marked Price} - 5\% \times \text{Marked Price} \] \[ \text{SP} = 760 - (0.05 \times 760) = 760 - 38 = 722 \] Step 3: Calculate the actual profit. \[ \text{Profit} = \text{SP} - \text{CP} = 722 - 633.33 = 88.67 \] Step 4: Find the actual profit percentage. \[ \text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{88.67}{633.33}\right) \times 100 \] \[ = 14.0\% \] Thus, the actual percentage profit is **14\%** (correct to 2 significant figures).