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Comparing Quantities - Profit and Loss, Discount, VAT

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Cost Price (CP) and Selling Price (SP): The Cost Price is the amount paid to purchase an article or the cost incurred to manufacture it. The Selling Price is the price at which the article is sold to a customer. Visually, if you think of a flow of money, CPCP is the 'input' and SPSP is the 'output'.

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Profit and Loss: If the Selling Price is greater than the Cost Price (SP>CPSP > CP), the difference is called Profit. If the Cost Price is greater than the Selling Price (CP>SPCP > SP), the difference is called Loss. In a balance scale visualization, Profit tilts the scale toward the SPSP side, while Loss tilts it toward the CPCP side.

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Profit or Loss Percentage: Profit or loss is always calculated as a percentage of the Cost Price (CPCP). This allows for a standardized comparison of gains or losses across different transactions. Think of it as a portion of the original 'investment' pie chart that was gained or lost.

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Marked Price (MP) and Discount: The Marked Price (also known as the List Price) is the price printed on an item or tagged by the retailer. A Discount is a reduction offered on this Marked Price to attract customers. Visually, imagine a price tag where the original MPMP is crossed out and a lower SPSP is written next to it.

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Discount Percentage: Discount is always calculated on the Marked Price (MPMP). It represents the percentage of the original tagged price that the customer does not have to pay. For example, a '20% Off' sign indicates that for every 100 units of currency on the price tag, 20 units are deducted.

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Sales Tax, VAT, and GST: These are taxes charged by the government on the sale of an item and collected by the shopkeeper from the customer. These taxes are calculated on the Selling Price (SPSP) and added to it to reach the final Bill Amount. Visually, this appears as an additional line item at the bottom of a grocery bill or invoice.

📐Formulae

Profit=SP−CPProfit = SP - CP

Loss=CP−SPLoss = CP - SP

Profit%=(ProfitCP×100)%Profit \% = (\frac{Profit}{CP} \times 100)\%

Loss%=(LossCP×100)%Loss \% = (\frac{Loss}{CP} \times 100)\%

SP=CP×(100+Profit%100)SP = CP \times (\frac{100 + Profit \%}{100})

SP=CP×(100−Loss%100)SP = CP \times (\frac{100 - Loss \%}{100})

Discount=MP−SPDiscount = MP - SP

Discount%=(DiscountMP×100)%Discount \% = (\frac{Discount}{MP} \times 100)\%

BillAmount=SP+(Tax%×SP100)Bill Amount = SP + (\frac{Tax \% \times SP}{100})

💡Examples

Problem 1:

A shopkeeper bought a chair for 750750 and sold it for 900900. Find his gain or loss percentage.

Solution:

  1. Identify values: CP=750CP = 750, SP=900SP = 900.
  2. Compare SPSP and CPCP: Since SP>CPSP > CP, it is a Profit.
  3. Calculate Profit: Profit=SP−CP=900−750=150Profit = SP - CP = 900 - 750 = 150.
  4. Calculate Profit Percentage: Profit%=(ProfitCP×100)%=(150750×100)%=(15×100)%=20%Profit \% = (\frac{Profit}{CP} \times 100)\% = (\frac{150}{750} \times 100)\% = (\frac{1}{5} \times 100)\% = 20\%.

Explanation:

First, we determine if the transaction resulted in a profit or loss by comparing the buying and selling prices. Since the selling price is higher, we calculate the profit amount and then find its percentage relative to the original cost price.

Problem 2:

An item is marked at 840840 and is sold for 714714. What is the discount and discount percentage?

Solution:

  1. Identify values: Marked Price (MPMP) = 840840, Selling Price (SPSP) = 714714.
  2. Calculate Discount: Discount=MP−SP=840−714=126Discount = MP - SP = 840 - 714 = 126.
  3. Calculate Discount Percentage: Discount%=(DiscountMP×100)%=(126840×100)%Discount \% = (\frac{Discount}{MP} \times 100)\% = (\frac{126}{840} \times 100)\%.
  4. Simplify: (126840×100)=126084=15%(\frac{126}{840} \times 100) = \frac{1260}{84} = 15\%.

Explanation:

The discount is the difference between what the tag says (MPMP) and what the customer actually pays (SPSP). To find the discount percentage, we divide the discount amount by the original marked price and multiply by 100.