Profit and Loss
What is Profit and Loss?
The original price paid for an item.
Key formula / rule: Profit
Key points
- Understand the concepts of Cost Price, Selling Price, Profit, and Loss.
- Calculate profit and loss percentages.
- Understand and calculate Marked Price and Discount.
- Solve problems involving multiple transactions or successive profits/losses.
Common exam trap
Calculating profit or loss percentage on the Selling Price instead of the Cost Price.
Definitions
- Term
Cost Price (CP)
- Meaning
The original price paid for an item.
- Term
Selling Price (SP)
- Meaning
The price at which an item is sold.
- Term
Profit
- Meaning
The financial gain when the selling price exceeds the cost price.
- Term
Loss
- Meaning
The financial decrease when the cost price exceeds the selling price.
- Term
Marked Price (MP)
- Meaning
The price displayed on an item, often higher than the CP, from which discounts are offered.
- Term
Discount
- Meaning
A reduction in price offered on the Marked Price.
Learning objectives
Understand the concepts of Cost Price, Selling Price, Profit, and Loss.
Calculate profit and loss percentages.
Understand and calculate Marked Price and Discount.
Solve problems involving multiple transactions or successive profits/losses.
Apply these concepts to real-world scenarios.
Formulae
- Name
Profit
- Note
Applicable when Selling Price is greater than Cost Price.
- Expression
Profit = SP - CP
- Name
Loss
- Note
Applicable when Cost Price is greater than Selling Price.
- Expression
Loss = CP - SP
- Name
Profit Percentage
- Note
Calculated on the Cost Price.
- Expression
Profit % = (Profit / CP) * 100
- Name
Loss Percentage
- Note
Calculated on the Cost Price.
- Expression
Loss % = (Loss / CP) * 100
- Name
Selling Price (with Profit)
- Note
Formula to find SP when CP and Profit % are known.
- Expression
SP = CP * (1 + Profit%/100)
- Name
Selling Price (with Loss)
- Note
Formula to find SP when CP and Loss % are known.
- Expression
SP = CP * (1 - Loss%/100)
- Name
Discount
- Note
The reduction offered on the Marked Price.
- Expression
Discount = MP - SP
- Name
Discount Percentage
- Note
Calculated on the Marked Price.
- Expression
Discount % = (Discount / MP) * 100
- Name
Selling Price (with Discount)
- Note
Formula to find SP when MP and Discount % are known.
- Expression
SP = MP * (1 - Discount%/100)
- Name
Relation between CP, SP, MP
- Note
Connects Cost Price, Selling Price, Marked Price, Profit/Loss, and Discount.
- Expression
CP * (1 ± Profit/Loss %) = MP * (1 - Discount %)
Prerequisites
Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
Fractions and Decimals
Percentage Calculations
Ratio and Proportion
Common mistakes
Calculating profit or loss percentage on the Selling Price instead of the Cost Price.
Confusing Marked Price with Cost Price.
Incorrectly applying discount calculations.
Not understanding the relationship between CP, SP, MP, and Discount.
Arithmetic errors in percentage calculations.
Keywords
Profit
Loss
Cost Price
Selling Price
Marked Price
Discount
Percentage
Profit Percentage
Loss Percentage
Discount Percentage
Successive Profit
Successive Discount
Practice preview
A sells an article to B at a profit of 20%. B sells it to C at a profit of 10%. If C pays Rs. 660 for the article, what was the cost price for A?…
medium
A merchant buys an item for Rs. 1200 and wants to make a profit of 20%. What should be the selling price?…
easy
A sells an article to B at a profit of 10%. B sells it to C at a profit of 20%. If C pays Rs. 660 for the article, what was the cost price for A?…
medium