Comparing Quantities Class 8 Notes given here has been carefully put together by experts to help students understand all the concepts given in chapter 8 clearly and at the same time allow them to practice sums effectively. The notes are further designed to help students complete timely revisions and score better marks in the exams. Some of the important topics covered in chapter 8 notes include;
- Introduction to areas of parallelograms and triangles.
- Finding the Increase or Decrease Percent
- Estimating Percentages
- Terms related to buying and selling
- Compound Interest
- Important Questions
The ratio is a quantitative measure that is used to determine the relation of two quantities or numbers further indicating how many times the first number contains the second. A ratio is usually used to compare the quantities.
For example; Find the ratio of 5 m to 20 km.
We know that 1 km = 1000m.
The required ration = 5 m / 10 km = 5m / ( 20 x 1000 m) = 1/4000.
Thus, the ratio of 5 m to 20 km is 1:4000
A percentage is a fraction of amount that is expressed as a particular number of hundredths of that amount. It is usually the ratio or the amount expressed as a fraction of 100. It is another means to compare the quantities.
Finding the Increase or Decrease Percent
To find the increase or decrease percent, multiply the percentage given by the actual quantity from which we need to increase or decrease. Then, to the actual quantity add or subtract the obtained quantity to get the final result.
Example: An employee now receives a salary of Rs. 60,000 after receiving a 15% hike. What was his previous salary?
Solution: Let the initial salary be n.
Generally, we write: initial salary + increment = new salary
Since the increment is 15%, thus we get
n + (15/100 x n ) = 60,000
Hence his previous salary was Rs. 53,480
There are several steps to be followed for estimating percentages. For instance, we need to find n percent of x then;
- Firstly, round off values of x and n to numbers whose simplification would be easy.
- These rounded numbers need to be multiplied.
- The answer of the multiplication has to be divided by 100.
Some Common Related Terms
- Cost Price (CP): This is the actual amount that a manufacturer allocates to generate a product or to provide the service.
- Selling Price (SP): The price at which a certain product is sold.
- Discount: The term refers to the reduction in the marked price of a product. Discount is always calculated on the marked price.
- Profit: The financial benefit that is acquired by selling a certain product. Profit is usually the difference between the cost price and the selling price.
- Loss: Loss basically refers to the negative revenue that is incurred on the sale of a product.
- Sales Tax (ST): The charge levied by the government of different products. Sales tax is mostly added to the selling price.
- GST: GST is levied on the supply of either goods or services or both.
Compound interest is the interest calculated on the principal amount as well as the interest earned till date.
The formula for computing Compound Interest is given as:
A = amount
P = principal amount
R = rate of interest
N = number of years
Applications of Compound Interest Formula
There are various situations where the CI needs to be calculated. Some of the common examples are stated below:
- (i) To find the rate of population growth.
- (ii) The rate at which bacteria grows.
- (iii) The increase or decrease in prices of products.
- Find the ratio of;
i. 5m to 20km ii. 100 paise to 5
- Convert the ratios to percentages
i. 2:5 ii. 4:6
- A wholesale shop offers a discount of 30 percent. What is the sale price of these items?
i. A mat marked at 125 ii. A slipper marked at 250 iii. A stove marked at 450
- Find the Selling price if there is a profit of 8% on;
i. A fan of 400 with 60 as overhead charges. ii. a toy bought at 450 and an expense of 100 made on its repair.
- Find CI on 15500 for 2 years at 11% per annum.