Revision Notes on Profit and Loss
Basic Concept Questions
- Definition: What is profit, and how is it different from loss?
- Calculation: If a product costs $50 and is sold for $70, what is the profit?
- Loss Calculation: If an item is purchased for $120 and sold for $100, what is the loss incurred?
Percentage Questions
- Profit Percentage: If a shirt is bought for $40 and sold for $60, what is the profit percentage?
- Loss Percentage: An article is bought for $80 and sold for $60. What is the loss percentage?
- Finding Cost Price: If a person sold a bicycle for $150 at a profit of 25%, what was the cost price?
Compound Questions
- Multiple Transactions: A shopkeeper bought three items for $30, $40, and $50, respectively. He sold them for $40, $50, and $80. What is the total profit or loss?
- Break-Even Analysis: If a business incurs fixed costs of $500 and sells a product for $20 with a variable cost of $10, how many units must be sold to break even?
Word Problems
- Discount and Profit: A retailer offers a 10% discount on a product that has a marked price of $200. If the cost price is $140, what is the profit made after the discount?
- Combined Profit: A man sells two articles for $300 each. The first was bought at a profit of 20%, and the second at a loss of 10%. What is his overall profit or loss?
Advanced Problems
- Partnership Scenario: Two partners invest $5,000 and $3,000 in a business. If the total profit is $2,000, how much will each partner receive?
- Loss in Percentage: If an item is sold at a 30% loss and the selling price is $70, what was the cost price?
Application-Based Questions
- Markup: A retailer wants to make a profit of 40% on an item that costs $60. What should be the selling price?
- Cost Price from Selling Price: If a book is sold for $15 at a loss of 25%, what was the cost price?
- Cost Price (CP): The price at which a product is purchased or produced.
- Selling Price (SP): The price at which a product is sold to customers.
- Profit or gain: When (SP) > (CP) then gain.
Gain = (SP) – (CP)
- Loss: When (SP) < (CP) then loss.
Loss = (CP) – (SP)
Example
If a shopkeeper bought 250 books for 75 each. He spent 500 Rs. on the binding of books. Then he sold it in 20000 Rs. Calculate the profit or loss percentage.
Solution:
Price of 250 books = 250 × 75 = 18750 Rs.
Cost price of books = 18750 + 500 = 19250 Rs.
Sale Price = 20000 Rs.
SP > CP so he made a profit.
Profit = SP – CP
= 20000 – 19250
= 750 Rs.
His profit on 19250 Rs. is 750 Rs.
Sales Tax/Value Added Tax/Goods and Services Tax
The amount charged by the government on the sale of an item is called Sales Tax.
Shopkeeper collects it from the customer and gives to the government. So the sales tax will always be on the selling price of the item and is added to the value of the bill.
Earlier you must have seen Sales tax on the bill, nowadays; you will mostly see Value Added Tax
Formula
If the tax is x%, then Total price after including tax would be
Example
If the sales tax of 5% is added to an item whose selling price is 1500 Rs then find the bill amount including tax.
Solution:
The tax amount = 5/100 x 1500 = 75 Rs
Hence, the bill amount = Selling Price + Tax
= 1500 Rs + 75 Rs
= 1575 Rs.