Inverse Proportion

What is a proportion ?

It is a statement that two ratios are equal.

Example :- 2:3 = 6:9

𝟔÷𝟑

𝟗÷𝟑 =

𝟐

𝟑

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No of Books

Price (Rs)

1 1:2 50 50:100=1:2

2 100

4 200 2:4=1:2

100:200=1:2

When one quantity increases according to a ratio, the other quantity also

increases in the same ratio

OR

When one quantity decreases according to a ratio the other quantity also

decreases in the same ratio

The two quantities are said to be directly proportional to each

other **************************

Speed

Time

When one quantity increases according to a ratio, the other quantity also

decreases in the same ratio

OR

When one quantity decreases according to a ratio the other quantity also

increases in the same ratio

The two quantities are said to be inversely proportional to each

other

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A vehicle with a uniform speed

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I. No of days taken by 8 men to complete the task = 9 days

No of days taken by 1 men to complete the task = 9 x 8 days

=72 days

II. Magnitude of the

task

= Amount of time required by 1

man

= 72 man days

III. Time taken to complete the task by 12 men =72 man days ÷12

=6 days

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Method 1

I. No of days , the food was sufficient for 12 cattle = 10 days

No of days , the food was sufficient for 1 cattle =

=

12 x10 days

120 days

II. If 12 cattle were there after 2 days , the remaining food is sufficient for 8

days.(10 days – 2 days)

Magnitude of the remaining food is 12 x 8 = 96 cattle days.

As 4 new cattle were brought, Then total no of cattle was 16.

The no. of days , the food was sufficient = 96 cattle days ÷ 16 cattle

= 6 days

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Method 2

NO OF CATTLE NO OF DAYS

12 10

1 x

Let us take the no of days the food was sufficient for 1 cattle as x .

They are inversely proportional. Then

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12:1 =

x: 10

12

1

= 𝑥

10

12 x 10 = 𝑥 x 1

120 = 𝑥

There fore for 120 days the food is sufficient.

Part I

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Part II If 12 cattle were there after 2 days, then 8 days are remaining. As 4 cattle were brought now

16 cattle are there. Let us take the no of days, the food is sufficient as y days.

NO OF CATTLE NO OF DAYS

12 8

16 y

12:16 = 8: y

12

16

= 𝑦

8

12 x 8 = 8 x 16

96 = 16 𝑦

96 ÷16

6

=

=

y

Now the food is sufficient for 6 days

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It takes 8 men 1 day to complete a certain task.

Then;

4 men need 2 days to complete the task.

2 men need 4 days to complete the task.

1 men need 8 days to complete the task.

Here No of men x No of days is a constant.

If x is the no of men and y is the no of days, then

X x y = k (k is a constant) x = 𝒌

𝒚 or y =

𝒌

𝒙

Representing inverse proportion algebraically

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Let us take the no days that 4 men will require as n.

Then ;

5 x 4 = k (k is a constant)

4 x n = k

5 x 4 = 4 x n

20 = 4n

5 = n

There fore 4 men will require 5 days.

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Sumedha College Gampaha

10 D students Copy this note into your note book and do the exercises in the text book

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