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Profit and Loss
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Today we'll explore the concepts of profit and loss. Who can tell me what profit is?
Profit is what you make after selling something for more than you bought it!
Exactly! Profit can be calculated using the formula \(Profit = S.P. - C.P.\). How about loss? What does that mean?
Loss is when you sell something for less than you bought it!
Correct! Loss is calculated using \(Loss = C.P. - S.P.\). Remember this with the mnemonic 'CPSP' – Cost Price minus Selling Price equals Loss!
Can you give us an example?
Sure! If you bought an item for $50 and sold it for $40, your loss is \(50 - 40 = 10\). That's a loss of $10.
What's the formula for calculating the profit percentage?
Great question! The formula is \(Profit\% = \frac{Profit}{C.P.} \times 100\). So if we made a profit of $10 on a CP of $50, it would be \(\frac{10}{50} \times 100 = 20\%\).
In summary, profit is what you earn, loss is what you lose, and we can quantify these with percentages!
Selling Price and Cost Price
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Now let's discuss selling price (S.P.) and cost price (C.P.). How can we calculate S.P. when we have profit?
You would add the profit to the cost price!
Exactly! The formula is \(S.P. = C.P. + Profit\). What about calculating C.P. when we have loss?
You subtract the loss from the selling price.
Right! The formula is \(C.P. = S.P. + Loss\). A good way to remember this: 'Add what you gain, subtract what you lose.'
What if we want to find out the cost price from selling price with profit?
When you have profit, the formula is \(C.P. = S.P. - Profit\). These formulas help us calculate the financial outcomes of our transactions!
In summary, selling price can be calculated by adding profit and cost price, while cost price can be derived by subtracting loss or profit from selling price.
Discount Calculation
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Let's move on to discounts! Can someone explain what a discount is?
A discount is a reduction from the marked price!
Correct! The formula for calculating discount is \(Discount = M.P. - S.P.\). What about finding the discount percentage?
That's \(Discount\% = \frac{Discount}{M.P.} \times 100\)!
Exactly! To remember this, think of 'How much off is the price?' That connects us to the discount percentage formula.
Can we have an example of a discount calculation?
Certainly! If an item has a marked price of $100 and is sold for $80, what's the discount?
It's $20!
Correct! And the discount percentage is \(\frac{20}{100} \times 100 = 20\%\).
So remember to calculate both the discount value and its percentage to gauge savings effectively!
Introduction & Overview
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Quick Overview
Standard
In this section, students learn essential formulae that are crucial for calculating profit, loss, selling price, cost price, discounts, and taxations like GST. Understanding these formulae enables students to apply mathematical principles in real-life financial scenarios effectively.
Detailed
Important Formulae in Commercial Mathematics
In commercial mathematics, mastering important formulae is crucial for effective financial decision-making. This section covers key formulae related to profit, loss, selling price, cost price, and discounts, which students can utilize when engaging in real-world financial situations.
Key Formulae Explained:
- Profit Percentage (
\(Profit\% = \frac{Profit}{C.P.} \times 100\)) indicates how much profit is made relative to the cost price. - Loss Percentage (
\(Loss\% = \frac{Loss}{C.P.} \times 100\)) shows the loss relative to the cost price. - Selling Price calculation:
- With Profit: \(S.P. = C.P. + Profit\)
- With Loss: \(S.P. = C.P. - Loss\)
- Cost Price determination:
- With Profit: \(C.P. = S.P. - Profit\)
- With Loss: \(C.P. = S.P. + Loss\)
- Discount can be derived from the marked price and selling price using \(Discount = M.P. - S.P.\). The percentage of discount is calculated as \(Discount\% = \frac{Discount}{M.P.} \times 100\).
Understanding these formulae allows students to make informed decisions in commercial contexts.
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Profit Percentage Formula
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● Profit% = ProfitC.P.×100\frac{\text{Profit}}{\text{C.P.}} \times 100
Detailed Explanation
The profit percentage formula helps us determine what percentage of the cost price (C.P.) is a profit. To calculate this, we take the profit amount and divide it by the cost price, then multiply by 100 to get a percentage. This shows how much profit was made compared to the original price paid for the item.
Examples & Analogies
Imagine you bought a toy for $50, and later sold it for $70. Your profit is $20. To find out the profit percentage: (Profit = $20, C.P. = $50). Therefore, Profit% = (20 / 50) * 100 = 40%. This means you made a 40% profit on your investment!
Loss Percentage Formula
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● Loss% = LossC.P.×100\frac{\text{Loss}}{\text{C.P.}} \times 100
Detailed Explanation
The loss percentage formula is used to calculate the percentage of loss incurred in a transaction. Similar to the profit percentage, we find the amount lost, divide it by the cost price, and then multiply by 100 to express it as a percentage. This helps quantify how much loss was experienced relative to the initial cost.
Examples & Analogies
Suppose you bought a book for $30 and had to sell it for $20 due to damage. Your loss is $10. To find the loss percentage: (Loss = $10, C.P. = $30). So, Loss% = (10 / 30) * 100 = 33.33%. This indicates you lost 33.33% of the amount you originally spent.
Selling Price with Profit
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● Selling Price = C.P. + Profit\text{C.P.} + \text{Profit}
Detailed Explanation
When calculating the selling price of an item, if you know the cost price (C.P.) and the profit you intend to make, you simply add the profit to the cost price. This gives the price at which you will sell the item to ensure a profit.
Examples & Analogies
If you buy a bicycle for $200 and want to make a $50 profit, the selling price will be determined by adding the profit to the cost. Selling Price = $200 + $50 = $250. So, you would sell the bicycle for $250.
Selling Price with Loss
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● Selling Price = C.P. − Loss\text{C.P.} - \text{Loss}
Detailed Explanation
In instances where a loss occurs, the selling price is calculated by subtracting the loss from the cost price. This formula shows how much you would charge for the item to minimize your losses.
Examples & Analogies
Imagine you purchased a jacket for $100 and, unfortunately, you have to sell it for $80, resulting in a loss of $20. To find the selling price: Selling Price = $100 - $20 = $80. This is the amount you would receive for the jacket.
Cost Price with Profit
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● Cost Price = S.P. − Profit\text{S.P.} - \text{Profit}
Detailed Explanation
When you know the selling price (S.P.) and the profit but need to figure out what the original cost price was, you can rearrange the formula. By subtracting the profit from the selling price, you can determine how much you initially paid for the item.
Examples & Analogies
If you sold a laptop for $900 and made a profit of $200, to find the cost price you would calculate: Cost Price = $900 - $200 = $700. This tells you that you bought the laptop for $700.
Cost Price with Loss
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● Cost Price = S.P. + Loss\text{S.P.} + \text{Loss}
Detailed Explanation
Conversely, if you sold something at a loss and know the selling price and the amount lost, you can find the cost price by adding the loss back to the selling price.
Examples & Analogies
For instance, if you sold a cellphone for $400 and had a loss of $100, to find the cost price you would use the formula: Cost Price = $400 + $100 = $500. You originally paid $500 for the cellphone.
Discount Calculation
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● Discount = M.P. − S.P.\text{M.P.} - \text{S.P.}
Detailed Explanation
This formula helps calculate the discount offered on a product. By subtracting the selling price (S.P.) from the marked price (M.P.), we find out how much of a discount was applied.
Examples & Analogies
If a pair of shoes is marked at $100 but sold for $80, the discount can be calculated as: Discount = $100 - $80 = $20. This indicates that a $20 discount was applied to the shoes.
Discount Percentage Formula
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● Discount% = DiscountM.P.×100\frac{\text{Discount}}{\text{M.P.}} \times 100
Detailed Explanation
To express the discount as a percentage of the original marked price, we use this formula. By dividing the discount amount by the marked price and then multiplying by 100, we get a clear percentage showing how much was saved.
Examples & Analogies
In the previous example where the shoes had a discount of $20 from the marked price of $100, the discount percentage is calculated as: Discount% = ($20 / $100) * 100 = 20%. This means the shoes were on a 20% discount.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Profit: The amount gained when the selling price exceeds the cost price.
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Loss: The amount lost when the selling price is less than the cost price.
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Marked Price: The original price before any discounts are applied.
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Discount: The reduction from the marked price indicating savings for the buyer.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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If an item is purchased for $50 and sold for $70, the profit is $20.
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An article with a marked price of $200 is sold for $160. The discount is $40, and the discount percentage is 20%.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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When buying things in sight, profit makes your pocket light, loss will take your money right.
📖 Fascinating Stories
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Imagine a merchant who buys fruits for a dollar each. He sells them for two. If he sells 10 for two dollars each, he gains $10, but if he sells them at one dollar, he loses.
🧠 Other Memory Gems
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C.P., S.P., Profit, Loss - remember 'Calculate Sales Profit Loss' when finding any of them.
🎯 Super Acronyms
Remember 'DCP' for Discounts, Cost Price, and Profit calculations!
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Cost Price (C.P.)
Definition:
The price at which an article is purchased.
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Term: Selling Price (S.P.)
Definition:
The price at which the article is sold.
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Term: Profit
Definition:
The amount gained when selling at a price higher than the cost price.
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Term: Loss
Definition:
The amount lost when selling at a price lower than the cost price.
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Term: Marked Price (M.P.)
Definition:
The initial price marked on the article before any discount is applied.
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Term: Discount
Definition:
A reduction in the marked price of an article.