Ratio | What is ratio?
A ratio is a
comparison between two quantities of same kind or same unit in terms of fraction
that shows how many times a quantity is of another quantity.
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The ratio of two numbers ‘a’ and ‘b’ is written as a/b
or a:b and is read as ‘a’ is to ‘b’. Similarly, ratio of ‘b’ and ‘a’ is written
as b/a or b:a. Usually, the ratio of two quantities is written in the lowest
term.
For example: Ratio between 40 kg and 70 kg is
calculated by dividing 40 kg and 70 kg. Thus, the ratio = 40 kg/70 kg = 4/7 =
4:7. A ratio is a unit less term.
In the ratio a/b, a is called the first term
(antecedent) and b is called the second term (consequent).
Workout Examples
Example 1: Find the ratio of:
a.
80
cm to 2 m
b.
400
gm to 5 kg
c.
40
seconds to 4 minutes
Solution: Here,
Example 2: Two numbers are in the ratio
of 3:5. If their sum is 48, find the numbers.
Solution: Here,
Ratio of two numbers =
3:5
Let, the numbers be 3x
and 5x
∴ 3x + 5x = 48
or, 8x = 48
or, x = 48/8
or, x = 6
∴ The numbers are: 3x =
3 × 6 = 18
5x = 5 × 6 = 30
Example 3: Two numbers are in the ratio
of 3:4. If 4 is added to each number, the ratio becomes 11:14, find the numbers
Solution: Here,
Ratio of two numbers =
3:4
Let, the numbers be 3x
and 4x
According to question,
(3x + 4)/(4x
+ 4) = 11/14
or, 11(4x + 4) = 14(3x + 4)
or, 44x + 44 = 42x +56
or, 44x – 42x = 56 – 44
or, 2x = 12
or, x = 12/2
or, x = 6
∴ The numbers are: 3x =
3 × 6 = 18
5x = 4 × 6 = 24
You can comment your
questions or problems regarding the ratio here.
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