# Direct and Inverse variations

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Category: Education

## Presentation Description

Made By- Munish Sharma TGT-Maths J.N.V. Una Himachal Pradesh

## Presentation Transcript

### Can you find the ratio of 5 Rs to 50 Paise ?:

Can you find the ratio of 5 Rs to 50 Paise ? How you read 2 : 3 :: 4 : 6 ? Solve 2 6 3 10 X What do you mean by variations ?

### Direct and Inverse Proportions:

Direct and Inverse Proportions Class – VIII th Name Of topic

### PowerPoint Presentation:

Direct and Inverse Variations

### Variation :

Variation The act of changing. The amount of a change. The extent or degree to which something varies is called variation.

### Direct Proportions:

Direct Proportions When we talk about a direct proportion, we are talking about a relationship where as x increases, y increases or x decreases, y decreases at a CONSTANT RATE .

### Some examples : :

Some examples : 1. If cost of 1 gel pen is Rs 10, then the what will be the cost of same 5 gel pens. Here as number of pens increased from 1 to 5 the cost of pens is also increased from Rs 10 to Rs 50 Ans. 50 Rs.

### PowerPoint Presentation:

2. If weight of 1 Maths. book is 500 gms then what will be the weight of 8 such books. Here as number of books increased from 1 to 8 the weight of Maths. books is also increased from 500 gms to 4000 gms. 4000 gms

### Such variations in which if one thing increases the other will also be increases at constant rate are called Direct Proportions:

Such variations in which if one thing increases the other will also be increases at constant rate are called Direct Proportions

### Examples of Direct Proportions:

Examples of Direct Proportions If no. of i tems purchased increases, the total cost also increases. As the no. of children increases their total weights also increases.

### Direct Proportion:

Direct Proportion In Direct Proportions we generally use the following formula: Quantity y 1 y 2 Cost x 1 x 2

### PowerPoint Presentation:

Example : If cost of 1 kg sugar is 30 Rs then what would be the cost of 5 kg sugar ? Ans. It is 150 Rs

### Similarly, we can find the cost of 8 kg or 10 kg sugar.:

Similarly, we can find the cost of 8 kg or 10 kg sugar. Weight of Sugar ( in Kg) 1 3 5 7 8 10 Cost ( in Rs) 30 90 150 210 240 300

### Some more examples of Direct Proportions:

Some more examples of Direct Proportions Petrol in Litres (x) 1 2 … 5 8 … Cost in Rs (y) 45 90 180 225 … 450 Find the Missing terms

### Problem 1. The cost of 5 metres of cloth is Rs 580. Find the cost of 12 metres of cloth.:

Problem 1. The cost of 5 metres of cloth is Rs 580. Find the cost of 12 metres of cloth. Length of cloth (in metres) 5 12 Cost (in Rs) 580 X 5 12 580 X

### 5 x X = 12 x 580:

5 x X = 12 x 580 12 x 580 5 X X 12 x 116 X 1392 Therefore cost of 12 mtr of cloth is Rs 1392

### Problem 2. A truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours ?:

Problem 2. A truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours ? Distance travelled (in kms) 14 X Time taken (in minutes) 25 300 14 X 25 300

### 25 x X = 14 x 300:

25 x X = 14 x 300 14 x 300 25 X X 14 x 12 X 168 Therefore distance travelled by truck in 5 hours is 168 Km.

### Some Problems Related To Direct Proportions:

Some Problems Related To Direct Proportions If the cost of 6 kg Apples is 252 Rs, then what will be the cost of 25 kg of Apples ? 2.A car moves 150 km with 9 liters of petrol. Then how much petrol is required to travel a distance of 450 km ? 3. If weight of 15 number of Maths books is 1kg 250 grams, then what will be the weight of 48 such books ?

### Inverse proportion:

Inverse proportion Inverse is opposite to direct. In an inverse as one value goes up , the other goes down in same ratio.

### PowerPoint Presentation:

Such variations in which if one thing increases the other will decreases at constant rate are called Inverse Proportions

### Some examples : :

Some examples : 1. If 5 workers can build a house in 48 hours, then 10 workers will build it in 24 hours ? Here as number of workers increases from 5 to 10 the time taken to build the house decreases from 48 hours to 24 hours.

### PowerPoint Presentation:

A car moving with a speed of 40 km/hr covers a fix distance in 10 min. If speed of car is increased to 80 km/hr then it covers the same distance in 5 minutes. Here as speed is increased from 40 km/hr to 80 km/hr the time taken is decreased from 10 min. to 5 minutes.

### Some more examples of Inverse Proportions:

Some more examples of Inverse Proportions Speed in km/hr 3 5 6 15 Time Taken in min. 30 18 15 6 Find the Missing terms

### Problem 1. If a box of sweets is divided among 24 children they will get 5 sweets each. How many each would get if children are 20.:

Problem 1. If a box of sweets is divided among 24 children they will get 5 sweets each. How many each would get if children are 20. No. of Children (x) 24 20 Sweet each child will get (y) 5 P 20 x P 24 x 5 x 1 y 1 = x 2 y 2

### PowerPoint Presentation:

24 x 5 20 P X 6 Therefore each child will get 6 sweets each. 20 x P 24 x 5

### Problem 2. If 6 men can white wash a house in 30 days, how many men are required to complete the same work in 12 days:

Problem 2. If 6 men can white wash a house in 30 days, how many men are required to complete the same work in 12 days Men (x) 6 P Days (y) 30 12 12 x P 6 x 30 x 1 y 1 = x 2 y 2

### PowerPoint Presentation:

6 x 30 12 P P 15 Therefore 15 men are required to complete the same work in 12 days 12 x P 6 x 30

### Recapitulation:

Recapitulation With Direct proportion we Divide our x’s and y’s. In Inverse proportion we will Multiply them. x 1 y 1 = x 2 y 2

### Home Assignments:

Home Assignments 6 pipes are required to fill a tank in 1 hour 20 minutes. How long will it take if only 5 pipes of same type are used ? 2. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day and school hours be same.

### 3. A machine in a soft drink factory fills 840 bottles in 6 hours. How many bottles will it fill in 5 hours ?:

3. A machine in a soft drink factory fills 840 bottles in 6 hours. How many bottles will it fill in 5 hours ?

### END OF SHOW:

END OF SHOW Presented By : Munish Sharma 