A percentage is a number or ratio expressed as a fraction of 100. The word percent means "per hundred" or "out of every 100". Percentages are used to compare quantities, calculate discounts, profits, losses, taxes, examination scores and many other real-life situations.
The symbol used for percentage is %.
Percentage is used in everyday life when:
Example
If a student scores 80% in a Mathematics examination, it means the student scored 80 marks out of every 100 marks.
Percentage Increase is the percentage by which a quantity becomes larger than its original value.
Percentage Increase Formula:
We get the percentage increase using the formula below:
Percentage Increase = Increase Original Value × 100%
In order to get increase, we subtract the original value from the new value ;
Increase = New Value - Original value
Example
The price of a bag increases from $40 to $50, find the percentage increase of the bag.
solution :
Step 1:Get the Increase
Original Price = $40
New price = $50
Increase = New price - Original Price
Increase = $50 - $40
Increase = $10
Since we have Increase, we can get the percentage Increase by using the formula:
Percentage Increase = Increase Original Value × 100%
Step 2: Substitute the values in the formula.
Percentage Increase = $10 $40 × 100%
Percentage Increase = 25%
Percentage Decrease is the percentage by which a quantity becomes smaller than its original value.
Percentage Decrease Formula:
We get the percentage decrease using the formula below:
Percentage Decrease = Decrease Original Value × 100%
In order to get decrease, we subtract the new value from the original value;
Decrease = Original Value - New Value
Example
The price of a television reduces from $800 to $680, find the percentage decrease of the television.
solution :
Step 1:Get the Decrease
Original Price = $800
New Price = $680
Decrease = Original Price - New Price
Decrease = $800 - $680
Decrease = $120
Since we have Decrease, we can get the percentage decrease by using the formula:
Percentage Decrease = Decrease Original Value × 100%
Step 2: Substitute the values in the formula.
Percentage Decrease = $120 $800 × 100%
Percentage Decrease = 15%
Percentage Profit is the profit made expressed as a percentage of the original cost price.
Percentage Profit Formula:
We get the percentage profit using the formula below:
Percentage Profit = Profit Cost Price × 100%
In order to get profit, we subtract the cost price from the selling price;
Profit = Selling Price - Cost Price
Example
A trader buys a bicycle for $250 and sells it for $320. Find the percentage profit of the bicycle.
solution :
Step 1:Get the Profit
Cost Price = $250
Selling Price = $320
Profit = Selling Price - Cost Price
Profit = $320 - $250
Profit = $70
Since we have Profit, we can get the percentage profit by using the formula:
Percentage Profit = Profit Cost Price × 100%
Step 2: Substitute the values in the formula.
Percentage Profit = $70 $250 × 100%
Percentage Profit = 28%
Percentage Loss is the loss incurred expressed as a percentage of the original cost price.
Percentage Loss Formula:
We get the percentage loss using the formula below:
Percentage Loss = Loss Cost Price × 100%
In order to get loss, we subtract the selling price from the cost price;
Loss = Cost Price - Selling Price
Example
A phone is bought for $600 but sold for $540, find the percentage loss of the phone.
solution :
Step 1:Get the Loss
Cost Price = $600
Selling Price = $540
Loss = Cost Price - Selling Price
Loss = $600 - $540
Loss = $60
Since we have Loss, we can get the percentage loss by using the formula:
Percentage Loss = Loss Cost Price × 100%
Step 2: Substitute the values in the formula.
Percentage Loss = $60 $600 × 100%
Percentage Loss = 10%
Percentage Discount is the reduction given on the original marked price of an item expressed as a percentage.
Percentage Discount Formula:
We get the percentage discount using the formula below:
Percentage Discount = Discount Amount Marked Price × 100%
In order to get discount amount, we subtract the selling price from the marked price;
Discount Amount = Marked Price - Selling Price
Example
A laptop marked at $1,000 is sold to a customer for $850, find the percentage discount given on the laptop.
solution :
Step 1:Get the Discount Amount
Marked Price = $1,000
Selling Price = $850
Discount Amount = Marked Price - Selling Price
Discount Amount = $1,000 - $850
Discount Amount = $150
Since we have Discount Amount, we can get the percentage discount by using the formula:
Percentage Discount = Discount Amount Marked Price × 100%
Step 2: Substitute the values in the formula.
Percentage Discount = $150 $1,000 × 100%
Percentage Discount = 15%
Percentage Commission is the payment earned by an agent or salesman for selling goods or services, expressed as a percentage of the total value of sales made.
Percentage Commission Formula:
We get the percentage commission using the formula below:
Percentage Commission = Commission Earned Total Sales Value × 100%
In order to get commission earned, we subtract the amount retained by the owner from the total sales value (or compute it directly from a given rate):
Commission Earned = Total Sales Value − Amount Retained by Owner
Example
A real estate agent sells a plot of land for $5,000 and receives a payout fee of $250 for organizing the transaction. Find the percentage commission given to the agent.
Solution:
Step 1: Get the Commission Earned
Total Sales Value = $5,000
Commission Earned = $250
Since we have Commission Earned, we can get the percentage commission by using the formula:
Percentage Commission = Commission Earned Total Sales Value × 100%
Step 2: Substitute the values in the formula.
Percentage Commission = $250 $5,000 × 100%
Percentage Commission = 5%
A student scored 72 marks out of a possible 90 marks in a Mathematics examination. Calculate the student's percentage score.
Step 1: Identify the given values.
Marks Obtained = 72
Total Marks = 90
We are required to calculate the percentage score.
Step 2: Write the Percentage formula.
Percentage = Marks Obtained Total Marks × 100%
Step 3: Substitute the values into the formula.
Percentage = 72 90 × 100%
The known values have been substituted correctly.
Step 4: Simplify.
Percentage = 0.8 × 100%
Percentage = 80%
This is the student's examination score.
Percentage = 80%
A supermarket purchased a refrigerator for $850 and later sold it for $1,020. Calculate the percentage profit made on the refrigerator.
Step 1: Identify the given values.
Cost Price = $850
Selling Price = $1,020
We are required to calculate the percentage profit.
Step 2: Calculate the Profit.
Profit = Selling Price − Cost Price
Profit = 1,020 − 850
Profit = $170
This is the money gained after selling the refrigerator.
Step 3: Write the Percentage Profit formula.
Percentage Profit = Profit Cost Price × 100%
Step 4: Substitute the values.
Percentage Profit = 170 850 × 100%
The calculated values have been substituted correctly.
Step 5: Simplify.
Percentage Profit = 0.2 × 100%
Percentage Profit = 20%
This is the percentage profit earned.
Percentage Profit = 20%
A television originally cost $1,250. During a clearance sale, the shop offered a 16% discount. Calculate the discount amount and the final selling price.
Step 1: Identify the given values.
Original Price = $1,250
Discount = 16%
We are required to calculate the discount amount and the final selling price.
Step 2: Write the formula for getting percentage discount.
Percentage Discount = Discount Amount Marked Price × 100%
Step 3: Make Discount the subject of the formula.
Discount = Percentage × Original Price 100
Step 4: Substitute the values.
Discount = 16 × 1,250 100
The given values have been substituted correctly.
Step 5: Simplify.
Discount = 20,000 ÷ 100
Discount = $200
This is the amount deducted from the original price.
Step 6: Calculate the Final Selling Price.
Final Price = Original Price − Discount
Final Price = 1,250 − 200
Final Price = $1,050
This is the amount paid after the discount.
Discount = $200
Final Selling Price = $1,050
A manufacturing company increased the monthly salary of one of its employees from $3,200 to $3,680. Calculate the percentage increase in the employee's salary.
Step 1: Identify the given values.
Original Salary = $3,200
New Salary = $3,680
We are required to calculate the percentage increase.
Step 2: Calculate the Increase.
Increase = New Salary − Original Salary
Increase = 3,680 − 3,200
Increase = $480
This is the amount by which the salary increased.
Step 3: Since we have the Increase, we calculate the percentage Increase using the formula :
Percentage Increase = Increase Original Value × 100%
Step 4: Substitute the values.
Percentage Increase = 480 3,200 × 100%
The known values have been substituted correctly.
Step 5: Simplify.
Percentage Increase = 0.15 × 100%
Percentage Increase = 15%
This is the percentage increase in the employee's salary.
Percentage Increase = 15%
A motor vehicle was purchased for $28,000. After several years of use, its market value decreased to $22,400. Calculate the percentage decrease in the value of the vehicle.
Step 1: Identify the given values.
Original Value = $28,000
New Value = $22,400
We are required to calculate the percentage decrease.
Step 2: Calculate the Decrease.
Decrease = Original Value − New Value
Decrease = 28,000 − 22,400
Decrease = $5,600
This is the amount by which the value decreased.
Step 3: Write the Percentage Decrease formula.
Step 4: Substitute the values.
The known values have been substituted correctly.
Step 5: Simplify.
Percentage Decrease = 0.2 × 100%
Percentage Decrease = 20%
This is the percentage decrease in the value of the vehicle.
Percentage Decrease = 20%
Attempt the following Questions:
(i) The population of a small rural town increases from 12,500 residents to 14,250 residents over a period of two years due to local industrial growth. Calculate the total increase in population and the percentage increase of the town.
(ii) A technology retail store decides to clear out old inventory by lowering the price of a gaming monitor from $400 down to $312. Find the absolute price decrease reduction amount and determine the percentage decrease applied to the monitor.
(iii) An electronics dealer purchases a wholesale bundle of smartphones for a cost price of $2,500. After selling all the units to consumers, the total revenue received is $3,200. Calculate the financial profit earned and find the percentage profit achieved by the dealer.
(iv) A business venture buys a commercial transport vehicle for a cost price of $12,000. Due to market depreciation and wear, they are forced to liquidate and sell the vehicle two years later for a selling price of $10,320. Determine the absolute financial loss and calculate the total percentage loss incurred.
(v) A designer clothing store marks a luxury leather jacket at an original price of $1,500. During an end-of-season promotional event, a buyer purchases the jacket with a discount and pays a final selling price of $1,245. Find the absolute discount markdown amount and calculate the percentage discount given.
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