NCERT Class 8 Maths: Comparing Quantities Ex 8.2

Welcome, Class 8 students! In Chapter 8, "Comparing Quantities," we learn how to make sense of numbers in our daily lives. Exercise 8.2 is a super important part of this journey, as it dives deep into real-world applications of percentages.

Here, you'll master concepts like calculating Profit and Loss when buying and selling items, understanding Discounts on your favourite products, and dealing with Sales Tax and Value Added Tax (VAT) that are added to your bills. These aren't just exam topics; they are essential life skills that help you make smart financial decisions, whether you're shopping, understanding a business, or managing money. By the end of this page, you will be confident in solving problems involving these practical percentage calculations, ready to tackle any question from your NCERT textbook and beyond!

Understanding Key Concepts: Profit, Loss, Discount, and Tax

Exercise 8.2 of Comparing Quantities introduces us to several crucial terms that help us analyse financial transactions. Let's break them down:

Cost Price (CP): This is the price at which an article is purchased. Think of it as the original price a shopkeeper pays for a product.
Selling Price (SP): This is the price at which an article is sold. This is what you pay to the shopkeeper.
Profit: If the Selling Price (SP) is greater than the Cost Price (CP), the seller makes a profit. Profit = SP - CP. Profit percentage is always calculated on the Cost Price: Profit % = (Profit / CP) × 100.
Loss: If the Selling Price (SP) is less than the Cost Price (CP), the seller incurs a loss. Loss = CP - SP. Loss percentage is also always calculated on the Cost Price: Loss % = (Loss / CP) × 100.
Marked Price (MP) or List Price: This is the price printed on the label or displayed on a product. It's often higher than the selling price to allow for discounts.
Discount: This is a reduction given on the Marked Price. Discounts make products more appealing to buyers. Discount = MP - SP. Discount percentage is always calculated on the Marked Price: Discount % = (Discount / MP) × 100.
Sales Tax (ST) / Value Added Tax (VAT): These are amounts charged by the government on the sale of goods and services. They are added to the Selling Price of the item, increasing the final amount the customer has to pay. The tax amount is usually a percentage of the selling price: Tax Amount = (Tax Rate / 100) × Selling Price. The final bill amount will be Selling Price + Tax Amount.

Understanding these definitions is the first step to mastering the problems in Exercise 8.2.

Step-by-Step Profit and Loss Calculations

Identify Cost Price (CP) and Selling Price (SP) — Carefully read the problem to determine the original purchase price (CP) and the price at which it was sold (SP).
Calculate Absolute Profit or Loss — If SP > CP, calculate Profit = SP - CP. If SP < CP, calculate Loss = CP - SP. If SP = CP, there's no profit or loss.
Calculate Percentage Profit or Loss — Always remember that profit or loss percentage is calculated with respect to the Cost Price (CP). Profit % = (Profit / CP) × 100 Loss % = (Loss / CP) × 100 For example, if CP = ₹400 and SP = ₹500: 1. CP = ₹400, SP = ₹500 2. Profit = ₹500 - ₹400 = ₹100 3. Profit % = (₹100 / ₹400) × 100 = (1/4) × 100 = 25%

Applying Discounts and Taxes

Example 1: Calculating Discount A bicycle is marked at ₹2500 and is sold at a 15% discount. What is the selling price? Step 1: Identify Marked Price (MP) and Discount Rate. MP = ₹2500, Discount Rate = 15%. Step 2: Calculate the Discount Amount. Discount = 15% of MP = (15/100) × ₹2500 = ₹375. * Step 3: Calculate the Selling Price (SP). SP = MP - Discount = ₹2500 - ₹375 = ₹2125. So, the bicycle is sold for ₹2125.
Example 2: Calculating Sales Tax / VAT A pair of shoes costs ₹800. If a 12% VAT is charged on it, what is the total amount to be paid? Step 1: Identify Selling Price (SP) and VAT Rate. SP = ₹800, VAT Rate = 12%. Step 2: Calculate the VAT Amount. VAT Amount = 12% of SP = (12/100) × ₹800 = ₹96. * Step 3: Calculate the Total Bill Amount. Total Amount = SP + VAT Amount = ₹800 + ₹96 = ₹896. The total amount to be paid for the shoes is ₹896.

YoLearn's Exam Tip: Avoid Common Mistakes!

When solving problems in Exercise 8.2, students often get confused about which base price to use for percentage calculations. Here's a quick guide to help you avoid common errors:

Profit and Loss Percentages: ALWAYS calculate Profit % or Loss % on the Cost Price (CP). Never on the Selling Price (SP) unless explicitly stated otherwise (which is rare in Class 8).
Discount Percentage: ALWAYS calculate Discount % on the Marked Price (MP) or List Price. Remember, discount is an offer from the seller on the displayed price.
Sales Tax/VAT: ALWAYS calculate Sales Tax or VAT on the Selling Price (SP) after any discounts have been applied. This is the price at which the item is actually sold to the customer before taxes are added.

Reading the question carefully and identifying CP, SP, and MP will save you from making these common, yet crucial, mistakes!

Practice Questions with Solutions

Q: A shopkeeper bought a table for ₹3500 and sold it for ₹4000. Calculate his profit percentage. A: Step 1: Identify CP and SP. CP = ₹3500, SP = ₹4000. Step 2: Calculate the profit. Profit = SP - CP = ₹4000 - ₹3500 = ₹500. Step 3: Calculate the profit percentage. Profit % = (Profit / CP) × 100 = (₹500 / ₹3500) × 100 = (1/7) × 100 = 14.28% (approx). Final answer: The shopkeeper's profit percentage is approximately 14.28%.
Q: An item was sold for ₹1200 at a loss of 20%. Find its cost price. A: Step 1: Understand the given information. SP = ₹1200, Loss % = 20%. Step 2: Use the formula relating SP, CP, and Loss %. If there is a loss of 20%, it means SP is (100 - 20)% of CP, which is 80% of CP. So, SP = 80/100 × CP. ₹1200 = 0.80 × CP. Step 3: Solve for CP. CP = ₹1200 / 0.80 = ₹1500. Final answer: The cost price of the item was ₹1500.
Q: A dress is marked at ₹1800. The shop offers a 25% discount. What is the selling price of the dress? A: Step 1: Identify Marked Price (MP) and Discount Rate. MP = ₹1800, Discount Rate = 25%. Step 2: Calculate the discount amount. Discount = 25% of MP = (25/100) × ₹1800 = ₹450. Step 3: Calculate the Selling Price (SP). SP = MP - Discount = ₹1800 - ₹450 = ₹1350. Final answer: The selling price of the dress is ₹1350.
Q: A refrigerator is priced at ₹15,000. If 8% GST (Goods and Services Tax) is added to the price, what is the final price a customer has to pay? A: Step 1: Identify the price before tax (SP) and the tax rate. SP = ₹15,000, GST Rate = 8%. Step 2: Calculate the GST amount. GST Amount = 8% of SP = (8/100) × ₹15,000 = ₹1200. Step 3: Calculate the final price. Final Price = SP + GST Amount = ₹15,000 + ₹1200 = ₹16,200. Final answer: The customer has to pay ₹16,200 for the refrigerator.

Frequently Asked Questions

What is the main difference between profit/loss percentage and discount percentage?

Profit/Loss percentage is calculated on the Cost Price (CP) and tells us how much gain or reduction a seller made relative to their original investment. Discount percentage, on the other hand, is calculated on the Marked Price (MP) and represents the reduction offered to the customer from the displayed price.

Why is Sales Tax/VAT added to the bill?

Sales Tax or VAT is added to the bill by the government as a levy on the sale of goods and services. It is a way for the government to collect revenue, and this tax is ultimately borne by the consumer, increasing the final price they pay.

Can an item have both a discount and a profit?

Yes, absolutely! A shopkeeper might offer a discount on the Marked Price (MP) to attract customers. However, if the Selling Price (after discount) is still higher than their Cost Price (CP), they will still make a profit. It's a common business strategy.

How do I know whether to calculate a percentage on CP, SP, or MP?

Always remember these rules: Profit or Loss percentage is calculated on the Cost Price (CP). Discount percentage is calculated on the Marked Price (MP). Sales Tax or VAT is calculated on the Selling Price (SP) after any discounts.