**Profit is the amount of money that a business earns after deducting all its expenses.**

**Loss is the amount of money that a business loses when its expenses exceed its earnings. **

**Discount is a reduction in the price of an item. It’s often used as an incentive to encourage customers to buy more of a product or to make a purchase at a particular time.**

**Profit, Loss, and Discount **

**Formulae**

**Profit formula: **

**Profit = Selling price – Cost price**

**Profit Percentage formula:**

**Profit percentage = (Profit / Cost price) x 100%**

**Cost price **

**Price at which the product was purchased**

**Selling price **

**Price at which the product was sold**

**Loss formula: **

**Loss = Cost price – Selling price**

**Loss Percentage formula**:

**Loss percentage = (Loss / Cost price) x 100%**

**Discount formula: **

**Discount = Original price x Discount rate**

**Discounted price = Original price – Discount**

**Sale price**

**Sale Price = Original Price – (Discount Rate x Original Price)**

**Original Price is the price before the discount.**

**Discount Rate is the percentage discount.**

**Cost Price**

**Cost Price = Selling Price / (1 + Profit Margin)**

**Selling Price is the sale price after the discount.**

**Profit Margin is the percentage profit margin.**

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**Step by Step Solutions to Sale Price and Cost Price Problems**

**Questions on Profit and Profit Percentage**

**Question 1: **

**If the cost price of a product is $50 and it is sold for $70, the profit and profit percentage would be:**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $70 – $50 = $20**

**Now calculate profit percentage**

**Profit percentage = (Profit / Cost price) x 100% **

**Profit percentage = ($20 / $50) x 100% = 40%**

**The profit percentage is 40%**

**Requested by: Ilyas**

**Question 2: **

**A toy store sells a toy for $12 that cost them $8. What is the profit percentage?**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $12 – $8 = $4**

**Profit percentage = (Profit / Cost price) x 100% **

**Profit percentage = ($4 / $8) x 100% = 50%**

**The profit percentage is 50%**

**Requested by: Ilyas**

**Question 3: **

**A company sells a product for $35 that cost them $30. What is the profit percentage?**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $35 – $30 = $5**

**Profit percentage = (Profit / Cost price) x 100% **

**Profit percentage = ($5 / $30) x 100% = 16.67%**

**The profit percentage is 16.67%.**

**Requested by: Ali Akbar**

**Question 4: **

**A shopkeeper sells a shirt for $50 that cost him $40. What is the profit percentage?**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $50 – $40 = $10**

**Profit percentage = (Profit / Cost price) x 100%**

**Profit percentage = ($10 / $40) x 100% = 25%**

**The profit percentage is 25%.**

**Requested by: Faizan**

**Question 5: **

**A car dealership sells a car for $20,000 that cost them $18,000. What is the profit percentage?**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $20,000 – $18,000 = $2,000**

**Profit percentage = (Profit / Cost price) x 100% **

**Profit percentage = ($2,000 / $18,000) x 100% = 11.11%**

**The profit percentage is 11.11%.**

**Requested by: Faizan**

**Question 6: **

**A bakery sells a cake for $40 that cost them $30. What is the profit percentage?**

**Solution:**

**Profit = Selling price – Cost price **

**Profit = $40 – $30 = $10**

**Profit percentage = (Profit / Cost price) x 100%**

**Profit percentage = ($10 / $30) x 100% = 33.33%**

**The profit percentage is 33.33%.**

**Requested by: Kareem**

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**Questions on Loss and Loss Percentage**

**Question 1: **

**A shopkeeper bought a book for $15 and sold it for $10. What is the loss percentage?**

**Solution:**

**Loss = Cost price – Selling price = $15 – $10 = $5**

**Loss percentage = (Loss / Cost price) x 100% = ($5 / $15) x 100% = 33.33%**

**The loss percentage is 33.33%.**

**Requested by: Enaam**

**Question 2: **

**If the cost price of a product is $100 and it is sold for $80, the loss and loss percentage would be:**

**Loss = Cost price – Selling price**

**Loss = $100 – $80 = $20**

**Now calculate the loss percentage**

**Loss percentage = (Loss / Cost price) x 100% **

**Loss percentage = = ($20 / $100) x 100% = 20%**

**The loss percentage is 20%.**

**Requested by: Raheel**

**Question 3: **

**A bookshop owner bought a book for $50 and sold it for $40. What is the loss percentage?**

**Solution:**

**Cost price of the book = $50**

**Selling price of the book = $40**

**Loss = Cost price – Selling price **

**Loss = $50 – $40 = $10**

**Loss percentage = (Loss/Cost price) x 100%**

**Loss percentage = (10/50) x 100% = 20%**

**The loss percentage is 20%.**

**Requested by: Ismail**

**Question 4: **

**A store owner purchased 50 chairs for $400 each. However, due to some damage, he had to sell them at $300 each. What is the total loss incurred by the store owner?**

**Solution:**

**Cost price of 50 chairs = 50 x $400 = $20,000**

**Selling price of 50 chairs = 50 x $300 = $15,000**

**Loss = Cost price – Selling price **

**Loss = $20,000 – $15,000 = $5,000 **

**The total loss incurred by the store owner is $5,000**.

**Requested by: Ahsan**

**Question 5:**

**A manufacturer sold a product for $240 and made a loss of 20%. What was the cost price of the product?**

**Solution:**

**Let the cost price of the product be ‘C’**

**Selling price of the product = $240**

**Loss percentage = 20%**

**Loss = (Loss percentage/100) x Cost price **

**Loss = (20/100) x C = 0.2C**

**Selling price = Cost price – Loss**

**$240 = C – 0.2C**

**$240 = 0.8C**

**C = $300**

**The cost price of the product was $300.**

**Requested by: Laiba**

**Question 6:**

**A merchant buys an item for $80 and sells it for $64. What is the loss percentage?**

**Solution:**

**Cost price of the item = $80**

**Selling price of the item = $64**

**Loss = Cost price – Selling price **

**Loss = $80 – $64 = $16**

**Loss percentage = (Loss/Cost price) x 100%**

**Loss = (16/80) x 100% = 20%**

**the loss percentage is 20%.**

**Requested by: Ismail**

**Question 7:**

**A factory produces 5000 pens at a cost of $10 per pen. Due to a manufacturing defect, it had to sell them for $8 per pen. What is the percentage loss?**

**Solution:**

**Cost price of 5000 pens = 5000 x $10 = $50,000**

**Selling price of 5000 pens = 5000 x $8 = $40,000**

**Loss = Cost price – Selling price **

**Loss = $50,000 – $40,000 = $10,000**

**Loss percentage = (Loss/Cost price) x 100%**

**Loss percentage = (10,000/50,000) x 100%= 20%**

**the percentage loss is 20%.**

**Requested by: Ismail**

**Question 8:**

**A shopkeeper sold an item for $80 and suffered a loss of 25%. What was the cost price of the item?**

**Solution:**

**Let the cost price of the item be ‘C’**

**Selling price of the item = $80**

**Loss percentage = 25%**

**Loss = (Loss percentage/100) x Cost price **

**Loss = (25/100) x C = 0.25C**

**Selling price = Cost price – Loss**

**Selling price = $80 = C – 0.25C**

**$80 = 0.75C**

**C = $106.67**

**The cost price of the item was $106.67.**

**Requested by: Ali Asghar**

**Questions on Discount and Discount Percentage**

**Question 1:**

**if a product originally costs $100 and is being offered at a 20% discount, the discounted price would be:**

**Discount = Original price x Discount rate**

**Discounted price = Original price – Discount**

**Discount = $100 x 0.20 = $20**

**Discounted price = $100 – $20 = $80**

**Requested by: Junaid**

**Question 2:**

**A shopkeeper sells an item at a discount of 20%. If the selling price of the item is $80, ****what is the original price of the item?**

**Solution:**

**Let the original price of the item be ‘P’**

**Discount percentage = 20%**

**Discount = (Discount percentage/100) x Original price **

**Discount = (20/100) x P = 0.2P**

**Selling price = Original price – Discount**

**$80 = P – 0.2P**

**$80 = 0.8P**

**P = $100**

**The original price of the item was $100.**

**Requested by: Kantesh Kumar**

**Question 3:**

**A store offers a discount of 15% on all items. If the original price of a product is $200, ****what is the selling price after the discount?**

**Solution:**

**Original price of the product = $200**

**Discount percentage = 15%**

**Discount = (Discount percentage/100) x Original price **

**Discount = (15/100) x $200 = $30**

**Selling price = Original price – Discount**

**Selling price = $200 – $30 = $170**

**The selling price after the discount is $170.**

**Requested by: Jamal**

**Question 4:**

**A company offers a discount of 25% on its products. If the selling price of a product after the discount is $120, what is the original price of the product?**

**Solution:**

**Let the original price of the product be ‘P’**

**Discount percentage = 25%**

**Discount = (Discount percentage/100) x Original price **

**Discount= (25/100) x P = 0.25P**

**Selling price = Original price – Discount**

**$120 = P – 0.25P**

**$120 = 0.75P**

**P = $160**

**The original price of the product was $160.**

**Requested by: Bilawal**

**Question 5:**

**A store offers a discount of 10% on all items. If the original price of a product is $50, ****what is the selling price after the discount?**

**Solution:**

**Original price of the product = $50**

**Discount percentage = 10%**

**Discount = (Discount percentage/100) x Original price **

**Discount = (10/100) x $50 = $5**

**Selling price = Original price – Discount**

**Selling price = $50 – $5 = $45**

**The selling price after the discount is $45.**

**Requested by: Farid**

**Question 6:**

**A company offers a discount of 30% on its products. If the original price of a product is $120, what is the selling price after the discount?**

**Solution:**

**Original price of the product = $120**

**Discount percentage = 30%**

**Discount = (Discount percentage/100) x Original price **

**Discount = (30/100) x $120 = $36**

**Selling price = Original price – Discount**

**Selling price = $120 – $36 = $84**

**The selling price after the discount is $84.**

**Requested by: Farid**

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**Profit, loss and Discount**

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