# Complete Guide For Class 8th Math Chapter 8: Comparing Quantities

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Chapter 8, “Comparing Quantities,” introduces students to ratios, percentages, and their applications in real-life situations like profit-loss calculations, discounts, and simple interest. This chapter equips students with essential skills to analyze and interpret quantitative relationships, crucial for financial literacy and decision-making.

In Chapter 8, “Comparing Quantities,” we delve into various concepts crucial for understanding how to compare and analyze different quantities. This chapter covers the fundamentals of ratios, percentages, profit and loss calculations, discounts, simple and compound interest, and more. Let’s explore these topics in detail.

**Recalling Ratios for Comparing Quantities**

**What is a Ratio?**

- A ratio is a way to compare two numbers, separated by a colon (:).

**Example:**

- The ratio of 8 and 12 can be written as 8:12 or as a fraction of 8/12. This is read as “eight is to twelve.”

**Problem Example:**

- The class has 18 boys and 20 girls. The ratio of boys to girls is 18:20, which simplifies to 9:10.

**Recalling Percentage**

**Understanding Percentages**

- A percentage expresses a number as a fraction of 100, denoted by the percent sign (“%”).

**Example:**

- 45% means 45 out of 100 or 0.45 as a decimal.

**Problem Example:**

- In a class of 24 boys and 26 girls, the percentage of boys is (24/50) x 100 = 48%, and the percentage of girls is (26/50) x 100 = 52%.

**Finding the Increase Percent**

**Calculating Increase**

- To find an increase, use the formula: Increase = (Increase % x Old amount) / 100
- New amount = Old amount + Increase

**Problem Example:**

- If petrol costs Rs 40 per liter in 2005 and increases by 10% in 2006, the new price is Rs 44.

**Finding the Decrease Percent**

**Calculating Decrease**

- To find a decrease, use the formula: Decrease = (Decrease % x Old amount) / 100
- New amount = Old amount – Decrease

**Problem Example:**

- A second-hand mobile with an original price of Rs 5000 is sold after a 20% price decrease, making the selling price Rs 4000.

**Discounts**

**Understanding Discounts**

- Discounts are reductions on the marked price of an item, often used to attract customers.

**Calculating Discounts:**

- Discount = Marked price – Sale price
- Discount % = (Discount / Marked price) x 100

**Problem Example:**

- A jacket marked at Rs 1000 is sold for Rs 900, resulting in a discount of Rs 100 and a discount percentage of 10%.

**Estimation in Percentages**

**Estimating Discounts**

- When calculating discounts on decimal values, you can estimate the amount to be paid.

**Problem Example:**

- For an item priced at Rs 785.70 with a 20% discount, the amount paid is approximately Rs 555.

**Prices Related to Buying & Selling**

**Key Terms:**

**Cost Price (C.P):**Price at which an item is bought.**Selling Price (S.P):**The price at which an item is sold.**Overhead Charges:**Expenses like repairs, labor, and transportation are included in C.P.

**Profit and Loss**

**Calculating Profit and Loss**

**Profit:**Occurs when S.P > C.P; Profit = S.P – C.P**Loss:**Occurs when C.P > S.P; Loss = C.P – S.P

**Profit % and Loss % Formulas:**

- Profit % = (Profit / C.P) x 100
- Loss % = (Loss / C.P) x 100

**Problem Example:**

- A man sells a second-hand TV at a loss of 35%.

**Taxes**

**Understanding Sales Tax and VAT**

- Sales tax is charged on the selling price and paid by the customer. VAT is included in the cost price itself.

**Problem Example:**

- A fridge costing Rs 13,000 with a 12% sales tax will have an additional Rs 1560 added to the bill.

**Simple Interest**

**Calculating Simple Interest**

- Simple Interest (S.I) = (Principal x Rate x Time) / 100
**Problem Example:**A man deposits Rs 9,000 at a 9% annual interest rate for 3 years, earning Rs 3240 as interest.

**Compound Interest**

**Understanding Compound Interest**

- Compound interest is calculated on the amount of the previous year, growing exponentially over time.

**Calculating Compound Interest:**

**Formula:**Amount = P(1 + R/100)^n**Problem Example:**Finding compound interest on Rs 10,000 for 2 years at 10% per annum.

**Rate Compounded Annually or Semi-Annually**

**Compounding Frequency**

- When interest is compounded semi-annually or quarterly, the time period and rate need to be adjusted accordingly.

**Problem Example:**

- Calculate the amount on a loan compounded semi-annually.

**Applications of Compound Interest Formula**

Now that we have a good understanding of comparing quantities we will see some real-life uses of these.

**Using the Formula in Real Life**

- The compound interest formula can be used to calculate population growth, item value appreciation or depreciation, and more.

**Modified Formula:**

- For calculating increased or decreased values over time using the rate of increase or decrease.

**Problem Example:**

- The depreciation of a scooter’s value over 2 years at a rate of 8% annually.

This chapter equips students with essential tools for understanding financial concepts, making informed decisions, and analyzing quantitative data in various contexts.

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