Comparing Quantities Class 8 Notes CBSE Maths Chapter 7 (Free PDF Download)

• Ratio:

• Ratio is the term for comparing through division. 

• The unit of ratio quantities is the same. 

• There is no unit for ratio. 

• Proportion is the equality of two ratios. It mean that,

$p:q$ are equal proportional to the $s:t$

That is

$\text{p : q :: s : t}$

$\dfrac{p}{q}=\dfrac{s}{t}$

• \[\text{Product of extremes = Product of means}\]

• Percentage:

• The term "percentage" refers to the number of people in a group of  $100$.

• A percentage is the outcome of any division with a divisor of $100$.

• Percentage can be calculated as;

$\text{Percentage = }\dfrac{\text{Value}}{\text{Total Value}}\text{ }\!\!\times\!\!\text{ 100}$

• The divisor is represented by the sign percent, which is read as percent.

• Profit And Loss:

1. Cost Price (CP): 

The cost price of an object is its initial unit purchase price.

2. Selling Price (SP):

Selling price is the amount a buyer pays for it.

• Overhead expenses are expenses incurred after the purchase of an item and are included in the cost price. These could include costs such as repair costs, labour costs, transportation, and so on.

• A discount is a reduction in the price of anything that has already been marked down.

\[\text{Discount = Marked Price - Sale Price}\]

The Marked price is the tagged price or list price which is the price on the label of an article or product.

This is the price at which the product will be offered for sale.

• When a discount $\%$ is specified, the discount can be calculated.

\[\text{Discount = Discount  }\%\text{  of Marked Price}\]

However, there may be a reduction applied to this price, and the product's real selling price may be lower than the marked price.

1. \[\text{Marked Price > Selling Price}\], when a discount is offered.

2. \[\text{Marked Price = Selling Price}\], when a discount is not available.

• Overhead expenses are expenses incurred after the purchase of an item and are included in the cost price.

\[\text{CP = Buying price + Overhead expenses}\]

• The government levies a sales tax on the sale of an item, which is then added to the total bill amount.

\[\text{Sales tax = Tax }\!\!%\!\!\text{  of Bill Amount}\]

• GST (Products and Services Tax) is a tax placed on the provision of goods, services, or both.

• Simple Interest: 

When the principal stays the same during the loan term, the interest paid is referred to as simple interest.

\[\text{SI = }\dfrac{\text{P }\times \text{ R }\times \text{ T}}{100}\]

• Compound Interest:

Compound interest is interest calculated on the sum from the previous year amount \[\text{A = }P+I\]

1. When Interest Is Compounded Annually, The Total Amount

\[\text{= P }{{\left( \text{1 + }\dfrac{\text{R}}{\text{100}} \right)}^{\text{n}}}\]

Where, \[P\] is principal, \[R\] is rate of interest and \[n\] is time period

2. When Interest Is Compounded Half-Yearly, The Amount

\[\text{= P }{{\left( \text{1 + }\dfrac{\dfrac{\text{R}}{2}}{\text{100}} \right)}^{\text{2n}}}\]

\[\dfrac{R}{2}\] is half-yearly rate and \[\text{2n = No. of ‘half-years’}\]

We compute the interest twice if the interest is compounded half-yearly. As a result, the time period is doubled and the rate is cut in half.

• Applications of Compound Interest:

In our daily life, the Compound Interest applicable for determining the following areas;

1. Population growth (or decline).

2. Bacterial growth if the rate of growth is known.

3. The value of an object if its price rises or falls over the course of several years.