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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