PROFIT AND LOSS
What are Profit and Loss?
Profit and loss are concepts used in business and finance to describe the financial outcomes of transactions or operations.
Profit:
- Profit is the financial gain obtained when the Selling Price (SP) of a product or service exceeds its Cost Price (CP).
- It's the positive difference between the revenue earned from selling goods or services and the cost incurred in producing or acquiring them.
- Mathematically: Profit=Selling Price (SP)−Cost Price (CP)
- Profit is a crucial metric for businesses as it represents the surplus income after covering expenses, indicating financial success.
Loss:
- Loss occurs when the Selling Price (SP) of a product or service is less than its Cost Price (CP).
- It's the negative difference between the cost incurred in acquiring or producing items and the revenue earned from selling them.
- Mathematically: Loss=Cost Price (CP)−Selling Price (SP)
- Losses indicate that the revenue generated is insufficient to cover the expenses incurred, leading to a deficit
Terms used in Profit and Loss
- Cost Price refers to the original price or the amount paid to purchase or produce a product or service. It is the expense incurred by a business or individual to acquire goods for sale
- Selling Price is the price at which a product or service is sold. It represents the revenue generated from the sale of goods or services.
- Profit is the financial gain obtained when the Selling Price (SP) exceeds the Cost Price (CP). It is the positive difference between the revenue earned and the cost incurred
- Loss occurs when the Selling Price (SP) is less than the Cost Price (CP). It is the negative difference between the cost incurred and the revenue generated
- Marked Price is the price at which a product or service is displayed or marked for sale. It might differ from the Selling Price due to discounts or promotional offers
- Profit Percentage is the percentage of profit earned concerning the Cost Price. It is calculated by dividing the profit by the Cost Price and multiplying by 100
- Loss Percentage is the percentage of loss concerning the Cost Price. It is calculated by dividing the loss by the Cost Price and multiplying by 100
- Discount is a reduction from the Marked Price, offered to customers to encourage sales. It decreases the Selling Price, affecting the overall profit or loss
- Margin refers to the difference between the Selling Price and the Cost Price. It can be a gross margin (without considering other expenses) or a net margin (after considering all expenses)
Profit and Loss Formulas
| Formula | Description | Usage |
|---|---|---|
| Profit: P = SP - CP | Calculates the total profit earned when the selling price (SP) is greater than the cost price (CP) | Profitable transactions |
| Loss: L = CP - SP | Calculates the total loss incurred when the cost price (CP) is greater than the selling price (SP) | Unprofitable transactions |
| Profit Percentage: P% = (P / CP) * 100 | Expresses the profit earned as a percentage of the cost price | Analyzing profitability or comparing profit across different products |
| Loss Percentage: L% = (L / CP) * 100 | Expresses the loss incurred as a percentage of the cost price | Analyzing losses or comparing loss across different products |
| Selling Price from Profit: SP = [(100 + P%) / 100] * CP | Finds the selling price required to achieve a desired profit percentage P% | Planning pricing strategies or calculating required selling price |
| Selling Price from Loss: SP = [(100 - L%) / 100] * CP | Finds the selling price required to minimize loss to L% | Minimizing losses or preventing further price reduction |
| Cost Price from Profit: CP = {100 / (100 + P%)} * SP | Finds the cost price associated with a given selling price SP and profit percentage P% | Analyzing profitability based on selling price and profit |
| Cost Price from Loss: CP = {100 / (100 - L%)} * SP | Finds the cost price associated with a given selling price SP and loss percentage L% | Analyzing losses based on selling price and loss |
| Marked Price (MP): MP = (100 + MP%) * CP | Calculates the marked price based on the cost price (CP) and mark-up percentage (MP%) | Implementing pricing strategies with discounts or mark-downs |
| Discount: D = MP - SP | Calculates the discount offered from the marked price (MP) to the selling price (SP) | Analyzing discounts or calculating required selling price after discount |
| Discount Percentage: D% = (D / MP) * 100 | Expresses the discount offered as a percentage of the marked price | Analyzing discount strategies or comparing discounts across different products |
For false weight, the profit percentage can be determined by the formula:
Gain%=Error/(TrueValue−Error)×100%.
Tips and Tricks on Profit and Loss
- Know the Basics: Have a clear understanding of Cost Price (CP), Selling Price (SP), profit, and loss definitions and relationships
- Quick Calculations: Practice mental math for basic calculations to save time in solving problems.
- Round-off Techniques: Round numbers to make calculations simpler while maintaining accuracy
- Understand Marked Price: Marked Price might differ from Selling Price due to discounts or promotional offers
- Real-life Examples: Apply profit and loss concepts to real-life scenarios to reinforce understanding.
- Variety of Problems: Practice solving different types of problems involving profit, loss, discounts, and profit percentage
- Graphs and Tables: Interpret graphs or tables representing profit and loss scenarios to derive conclusions.
- Word Problems: Extract information from word problems and apply appropriate formulas to solve them
- Use Study Materials: Refer to textbooks, online resources, and practice books to find diverse problems for practice
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Practice Questions on Profit and Loss
1.If the cost price of an item is $50 and it is sold for $70, calculate the profit percentage. Solution: Given: Cost Price (CP) = $50 Selling Price (SP) = $70 Profit = SP - CP = $70 - $50 = $20 Profit Percentage = ProfitCP×100=2050×100=40% Answer: The profit percentage is 40% 2.A bookshop sells a book for $180, incurring a loss of 10%. Calculate the cost price of the book. Solution: Given: Selling Price (SP) = $180 Loss Percentage = 10% Let CP be the cost price. Loss = Loss Percentage100×CP=10100×CP=110×CP Given that loss is 10%, which is $\frac{1}{10}$ of the cost price. Loss = CP - SP = CP - $180 CP - $180 = 110×CP Multiplying by 10 on both sides to eliminate the fraction: 10CP - $1800 = CP Rearranging the terms: 10CP - CP = $1800 9CP = $1800 CP = $1800 / 9 CP = $200 Answer: The cost price of the book is $200 3.A laptop is bought for $800 and sold for $1000. Calculate the profit percentage. Solution: Given: Cost Price (CP) = $800 Selling Price (SP) = $1000 Profit = SP - CP = $1000 - $800 = $200 Profit Percentage = Profit/CP×100=200/800×100=25% Answer: The profit percentage is 25% |
