Variations

Variation A change in one factor brings about a change in the related factor. These changes are termed as variation.

Examples of Variation What happens when......... You buy more pens ↑ ? Costs you more ↑ Number of students are more ↑? More number of teachers ↑ Speed of the car increases ↑? Time taken to reach destination decreases ↓ Number of people working increases ↑? Time taken to finish work decreases ↓

Direct Variation Answer: As the number of people living in the house What happens when.......... When you buy more pens , do you think that the total cost will increase or decrease? Answer: As you buy more pens ↑, total cost also increases ↑. When the number of people living in house decreases, do you think that the total weekly expense will increase or decrease? Answer: As the number of people living in the house decreases ↓, the weekly expense also decreases ↓.

Direct Variation Now, look at the following tables: Cost of 1 chocolate (Rs) 5 20 ↑ 30 ↑ Cost of 10 chocolates (Rs) 5 x 10 = 50 20 x 10 = 200 ↑ 30 x 10 = 300↑ For one to many, we need to multiply As the cost of 1 chocolate increases ↑, the cost of 10 chocolates also increases ↑ correspondingly. Cost of 5 Shirts (Rs) 3000 2000 1000 ↓ ↓ Cost of 1 Shirt (Rs) ↓ ↓ As the cost of 5 shirts decreases ↓ , the cost of 1 shirt also decreases ↓ correspondingly. For many to one, we need to divide

Direct Variation increase (↑ ) in the other quantity   When an increase (↑ ) in one quantity brings about an increase (↑ ) in the other quantity and similarly a decrease (↓) in one quantity brings about a decrease (↓) in the other quantity, then the two quantities are said to be in direct variation.

Some Direct variation examples: No of students in a class ↑ No of teachers ↑ Distance travelled by the car ↑ Time taken by the car ↑ No of chocolates purchased↓ Total expenses ↓ Amount deposited in the bank ↑ Interests for that amount ↑

Inverse Variation What happens when.......... When the speed of the car Increases , do you think that the time taken to reach the destination will increase or decrease? Answer: As the speed of the car increases ↑, the time taken to reach the given destination definitely decreases ↓. When the number of men decreases, do you think the days taken to complete the required job will increase or decrease? Answer: As the number of men decreases ↓, the days taken to complete the required job will definitely increases ↑.

Inverse Variation When an increase (↑) in one quantity produces a proportionate decrease (↓) in another quantity and similarly if a decrease (↓) in one quantity produces a proportionate increase (↑) in another quantity we say that the two quantities are in inverse variation.

Some Inverse variation examples: Planting of trees ↓ Temperature ↑ Speed of the car ↑ Time taken to travel ↓ No of lines per page ↑ No of pages ↓

Example 1: Identify the statement below is direct or inverse variations? Time and distance covered Solution: As time increases(↑) distance covered also increases(↑), Similarly if time decreases (↓) distance covered also decreases(↓), Hence it is Direct variation.

Example 2: Identify the statement below is direct or inverse variations? Number of men and time to complete a job Solution: As the number of men increases (↑), the days taken to complete a job will decrease (↓) Similarly as the number of men decreases (↓), the days taken to complete a job will increase (↑), Hence it is Inverse variation.

Try these Identify the statement below is direct or inverse variations? Number of pencil and its cost Number of lines per page and number of pages in book length of side of a square and its area Speed and time to cover a distance