Proportion | What is proportion?
Proportion is
the equality of two or more than two ratios. Four numbers a, b, c and d are
said to be in proportion if the ratio of a and b is equal to the ratio of c and
d. This is written as a:b::c:d and
read as ‘a is to b is as c is to d’.
First term and fourth term are called extremes
while second and third terms are called means.
In proportion, the product of extremes is always equal to
the product of means. That is a×d = b×c.
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Types of Proportions
There are 2 types of proportions; they are:
a. Direct proportion
b.
Indirect proportion
Direct proportion
If two quantities are so related that the increase or
decrease in one causes the corresponding increase or decrease in the other,
they are said to be direct proportion. Let us take an example of no. of copies
and their cost:
No. of Copies
|
Total Price (Rs.)
|
1
|
50
|
3
|
150
|
Ratio of copies = 1/3
Ratio of cost = 50/150 = 1/3
Here, the ratio of copies = ratio of cost i.e if number
of copies increases their cost also increase. So they are said to be in direct
proportion.
Indirect proportion
If two quantities are so related that the decrease or
increase in one causes the corresponding increase or decrease in the other is
called indirect (inverse) proportion. Let us take an example of no. of men and
their working days:
No. of men
|
No. of days
|
1
|
16
|
2
|
8
|
Ratio of men = 1/2
Inverse ratio of days = 8/16 = 1/2
Here, the ratio of men = inverse ratio of days i.e if
number of men increases their working days decreases. So they are said to be in
indirect proportion.
Workout Examples
Example 1: Find whether 5, 7, 20 and 28
are in proportion or not.
Solution: Here,
Product of extremes = 5
× 28 = 140
Product of means = 7 ×
20 = 140
Since, product of extremes = product
of means, the terms 5, 7, 20 and 28 are in proportion.
Example 2: Find the value of x if 5, x,
10 and 12 are proportional.
Solution: Here,
Product of extremes = 5
× 12 = 60
Product of means = x ×
10 = 10x
Since, the terms are proportional,
product of means = product of extremes
i.e. 10x
= 60
or, x
= 60/10
or, x
= 6
Example 3: If the terms 4, 5 and 8 are
three terms of proportion, find the fourth proportion.
Solution: Let x be the fourth proportion.
Now, 4, 5, 8 and x are
in proportion.
∴ 4/5 = 8/x
or, 4x = 40
or, x = 40/4
or, x = 10
∴ The fourth
proportion is 10.
Example 4: If the cost of 18 kg of rice
is Rs. 720, find the cost of 5 kg of rice.
Solution: Let x be the cost of 5 kg of rice.
Rice (kg)
|
Cost (Rs.)
|
18
|
720
|
5
|
x
|
Since quantity of rice and their
cost are in direct proportion,
∴ 18/5 = 720/x
or, 18x = 3600
or, x = 3600/18
or, x = 200
∴ Cost of 5 kg of rice is Rs. 200.
Example 5: A group of 400 men has
provision for 90 days. For how many men would the provision last for 60 days?
Solution: Let the provision last for 60 days for x men.
No. of Men
|
No. of Days
|
400
|
90
|
x
|
60
|
Since no. of men and days are in
indirect proportion,
∴ 400/x = 60/90
or, 60x = 400 × 90
or, x = 400 × 90/60
or, x = 600
∴ The required number of men is 600.
You can comment your
questions or problems regarding proportion here.
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