Profit, Loss and Discount Chapter Notes | Mathematics Class 8 ICSE PDF Download

Introduction

This chapter introduces the concepts of profit, loss, and discount, which are essential in understanding financial transactions in business and trade. It covers how to calculate profit or loss when buying and selling items, the impact of additional expenses like transportation, and how discounts and taxes affect the final price. The chapter also explains Value Added Tax (VAT) and how it is applied at different stages of a transaction. 

Key Terms

• Profit: Occurs when the selling price (S.P.) of an item is higher than its cost price (C.P.).
• Profit Formula: Profit = Selling Price - Cost Price (Profit = S.P. - C.P.).
• Loss: Occurs when the selling price is lower than the cost price.
• Loss Formula: Loss = Cost Price - Selling Price (Loss = C.P. - S.P.).
• Selling Price Calculation:
  • If profit: S.P. = C.P. + Profit
  • If loss: S.P. = C.P. - Loss
• Cost Price Calculation:
  • If profit: C.P. = S.P. - Profit
  • If loss: C.P. = S.P. + Loss
• Profit Percentage: Profit % = (Profit / C.P.) × 100%
• Loss Percentage: Loss % = (Loss / C.P.) × 100%
• Key Note: Profit and loss percentages are always calculated based on the cost price.
• Special Case: When the cost price and selling price are given for different quantities of items, first find the cost price and selling price for one item, then calculate the profit or loss.
• Number of Items for Specific Profit: Number of items = Total profit / Profit per item.

Overhead Expenses

• Definition: Overhead expenses refer to additional costs that are incurred when purchasing an item, such as transportation, labour, or packaging.
• Total Cost Price: The total cost price (C.P.) of an item is calculated by adding the actual cost price to the overhead expenses.
• Profit/Loss Calculation: Profit or loss is determined based on the total cost price, which includes overhead expenses.

To Find S.P., When C.P. and Gain (or Loss) Percent Are Given

Method 1: Step-by-Step

• Calculate gain or loss amount: Gain = (Gain % × C.P.) / 100 
• or Loss = (Loss % × C.P.) / 100.
• If gain: S.P. = C.P. + Gain.
• If loss: S.P. = C.P. - Loss.

Method 2: Direct Formula

• For gain: S.P. = [(100 + Gain %) / 100] × C.P.
• For loss: S.P. = [(100 - Loss %) / 100] × C.P.

To Find C.P., When S.P. and Gain (or Loss) Percent Are Given

Method 1: Step-by-Step

• Calculate gain or loss amount based on S.P. if given as a fraction of S.P.
• If there is a gain: Cost Price (C.P.) = Selling Price (S.P.) - Gain
• If there is a loss: Cost Price (C.P.) = Selling Price (S.P.) + Loss

Method 2: Direct Formula

• For gain: C.P. = [100 / (100 + Gain %)] × S.P.
• For loss: C.P. = [100 / (100 - Loss %)] × S.P.

Discount

• Definition: A discount is a reduction applied to the marked price (M.P.) of an item, typically used to facilitate the sale of old or damaged goods.
• Selling Price: The selling price (S.P.) is calculated by subtracting the discount from the marked price: S.P. = M.P. - Discount.
• Discount Formula: The discount can be calculated using the formula: Discount = M.P. - S.P.
• Discount Percentage: When the discount is expressed as a percentage (d%), the selling price can be calculated as: S.P. = [(100 - d) / 100] × M.P.
• Marked Price Calculation: The marked price can be determined from the selling price and discount percentage using the formula: M.P. = [100 / (100 - d)] × S.P.
• Alternative Name: The marked price is also known as the list price or printed price.

Tax

• Purpose: Taxes are levied by governments to fund facilities, infrastructure, administrative expenses, and welfare schemes.
• Tax Calculation: Tax is determined based on the selling price.
• Tax Formula: The formula for calculating tax is: Tax = (Rate of Tax × Sale Price) / 100.
• Total Amount Paid: The total amount paid is the sum of the sale price and the tax: Total amount = Sale Price + Tax.
• Direct Method: Alternatively, the total amount can be calculated using the direct method: Total amount = Sale Price × [(100 + Rate of Tax) / 100].
• Tax Rate Calculation: The rate of tax can be calculated as: Rate of Tax = (Tax / Sale Price) × 100.
• Note: Tax rates vary by item and state; some essential items may be exempt from tax.

Computation of Tax

• Tax Calculation: Tax = (Rate of Tax × Sale Price) / 100.
• Total Amount Paid: Total amount = Sale Price + Tax.
• Direct Method: Total amount = Sale Price × [(100 + Rate of Tax) / 100].
• Tax Rate: The Rate of Tax can be determined by the formula: Rate of Tax = (Tax / Sale Price) × 100.
• Finding Sale Price: When the total amount and the tax rate are known, the Sale Price can be computed as: Sale Price = Total amount × [100 / (100 + Rate of Tax)].
• Finding Tax Rate: If the total amount and Sale Price are available, Tax can be found by Tax = Total amount - Sale Price. Then, the Rate can be calculated using: Rate = (Tax / Sale Price) × 100.

Value-Added Tax (VAT)

• Definition: A tax collected at every stage of sale from the manufacturer to the retailer.
• VAT Calculation: VAT = Tax charged on sale - Tax paid on purchase.
• Alternative: VAT = Tax on value added, where value added = S.P. - C.P.
• Tax Paid: Tax paid = (Tax rate × Purchase price) / 100.
• Tax Charged: Tax charged = (Tax rate × Selling price) / 100.
• Key Note: VAT is the difference between the tax collected on sale and the tax paid on purchase, deposited to the government.