Direct and Inverse variations

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

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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

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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.

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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

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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.

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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.

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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

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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

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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

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