Learn the Ratio Formula with easy examples. Understand how to simplify ratios, convert fractions, decimals and percentages into ratios, and find unknown values in ratio questions. So, let us start with.
What is the Ratio Formula?
As already explained in our Ratio and Proportion section, the ratio formula is used to compare two quantities of the same kind.
It is usually represented in the following form:
Ratio Formula = First Quantity / Second Quantity
or
a : b = a/b (Basic ratio formula)
For example, if there are 20 boys and 30 girls in a class, then the ratio of boys to girls can be represented as:
Boys : Girls = 20 : 30
= 2 : 3
Thus, the ratio formula helps us compare one quantity with another.
Formula to Simplify Ratio
Often, we may come across questions where the ratio is not given in its simplest form. In such cases, this formula helps us simplify the ratio.
a : b = (a divided by HCF) : (b divided by HCF)
Here, HCF = Highest Common Factor
Example 1:
Simplify the ratio 36 : 48.
HCF of 36 and 48 = 12
Using the ratio simplification formula,
36 : 48
= (36/12) : (48/12)
= 3 : 4
Therefore, the simplified ratio is 3 : 4.
Example 2:
Simplify the ratio 45 : 60.
Answer:
HCF of 45 and 60 = 15
Using the ratio simplification formula,
45 : 60
= (45/15) : (60/15)
= 3 : 4
Therefore, the simplified ratio is 3 : 4.
Example 3:
Simplify the ratio 84 : 126.
Answer:
HCF of 84 and 126 = 42
Using the ratio simplification formula,
84 : 126
= (84/42) : (126/42)
= 2 : 3
Therefore, the simplified ratio is 2 : 3.
Formula to Convert Fraction into Ratio
We may come across questions where a fraction is given and we are asked to convert it into a ratio. In such cases, we can use the following formula:
a/b = a : b
Example 1:
Convert the fraction ⅗ into a ratio.
Here,
3 = Numerator (First Quantity)
5 = Denominator (Second Quantity)
Therefore,
3/5 = 3 : 5
Example 2:
Convert the fraction 18/24 into a ratio.
Answer:
18/24
= 18 : 24
HCF of 18 and 24 = 6
= (18/6) : (24/6)
= 3 : 4
Therefore, the ratio is 3 : 4.
Example 3:
The ratio of boys to girls in a class is represented by the fraction 48/72. Express it in ratio form and simplify it.
Answer:
48/72
= 48 : 72
HCF of 48 and 72 = 24
= (48/24) : (72/24)
= 2 : 3
Therefore, the ratio of boys to girls is 2 : 3.
Formula to Convert Decimal into Ratio
We may come across questions where a decimal number is given and we are asked to convert it into a ratio. In such cases, first convert the decimal into a fraction and then simplify it.
Decimal → Fraction → Simplify → Ratio
Example 1:
Convert 0.6 into a ratio.
Answer:
0.6
= 6/10
= 3/5
Therefore,
0.6 = 3 : 5
Example 2:
Convert 1.25 into a ratio.
Answer:
1.25
= 125/100
= 5/4
Therefore,
1.25 = 5 : 4
Example 3:
Convert 2.875 into a ratio.
Answer:
2.875
= 2875/1000
HCF of 2875 and 1000 = 125
= (2875/125) : (1000/125)
= 23 : 8
Therefore,
2.875 = 23 : 8
Formula to Convert Percentage to Ratio
We may also come across questions where a percentage is given and we are asked to convert it into a ratio. Such questions are frequently asked in SSC, RRB, Defence, Police, NDA, CDS and Banking examinations.
To convert a percentage into a ratio, first write the percentage as a fraction by dividing it by 100 and then simplify it.
Percentage → Fraction → Simplify → Ratio
You can also check our Basic Percentage section and Percentage to Fraction section to practice more such questions.
Example 1:
Convert 25% into a ratio.
Answer:
25%
= 25/100
HCF of 25 and 100 = 25
= (25/25)/(100/25)
= 1/4
Therefore,
25% = 1 : 4
Example 2:
Convert 40% into a ratio.
Answer:
40%
= 40/100
HCF of 40 and 100 = 20
= (40/20)/(100/20)
= 2/5
Therefore,
40% = 2 : 5
Example 3:
Convert 62.5% into a ratio.
Answer:
62.5%
= 62.5/100
= 625/1000
HCF of 625 and 1000 = 125
= (625/125)/(1000/125)
= 5/8
Therefore,
62.5% = 5 : 8
Formula to Find Unknown Variable in Ratio
Sometimes we may know the ratio but one quantity may be missing. In such cases, we can use the ratio formula to find the unknown variable.
Example 1:
If a : b = 2 : 3 and b = 18, find a.
Answer:
a/b = 2/3
a/18 = 2/3
3a = 36
a = 12
Therefore, a = 12.
Example 2:
If x : y = 5 : 8 and x = 25, find y.
Answer:
25/y = 5/8
5y = 25 × 8
y = 40
Example 3:
The ratio of boys and girls in a class is 3 : 5.
If there are 24 boys, find the number of girls.
Answer:
3 : 5
24 : x
24/x = 3/5
3x = 120
x = 40
Therefore, the number of girls is 40.
Formula to Divide a Quantity in a Given Ratio
We may come across questions where a quantity is given and we are asked to divide it in a specified ratio. In such cases, we can use the following formula:
If a quantity Q is divided in the ratio A : B, then
First Share
= [A/(A + B)] × Q
Second Share
= [B/(A + B)] × Q
Example 1: Divide ₹400 between Tom and Harry in the ratio 3 : 5.
Answer
Here,
Q = ₹400
Tom : Harry = 3 : 5
Total Parts
= 3 + 5
= 8
Tom’s Share
= [3/(3 + 5)] × 400
= (3/8) × 400
= ₹150
Harry’s Share
= [5/(3 + 5)] × 400
= (5/8) × 400
= ₹250
Therefore, Tom receives ₹150 and Harry receives ₹250.
Mean Proportional Formula and its Example of Application
a : b = b : c
Notice that b is repeated in both ratios. It lies between a and c, so it is called the mean proportional.
a/b = b/c
ac = b²
Mean Proportional (b) = √ac
Example
Find the mean proportional between 8 and 18.
Mean Proportional
= √(8 × 18)
= √144
= 12
Third Proportional Formula and its Example of Application
a : b = b : c
Notice that b is repeated in both ratios. The second term of the first ratio and the first term of the second ratio are the same.
Since c is the third term in the proportion, it is called the third proportional.
a/b = b/c
ac = b²
Third Proportional (c) = b²/a
Example
Find the third proportional to 4 and 18.
4 : 18 = 18 : x
x = 18²/4
= 324/4
= 81
Fourth Proportional Formula and its Example of Application
a : b = c : d
Notice that no term is repeated.
Since d is the fourth term in the proportion, it is called the fourth proportional.
a/b = c/d
ad = bc
Fourth Proportional (d) = (b × c)/a
Example
Find the fourth proportional to 4, 12 and 18.
4 : 12 = 18 : x
x = (12 × 18)/4
= 216/4
= 54
Compound Ratio Formula and its Application?
X : Y and A : B are two ratios, then
Compound Ratio
= (X × A) : (Y × B)
If there are three ratios,
X : Y
A : B
C : D
then
Compound Ratio
= (X × A × C) : (Y × B × D)
Example
Find the compound ratio of:
3 : 4 and 5 : 6
Compound Ratio
= (3 × 5) : (4 × 6)
= 15 : 24
= 5 : 8
Therefore,
Compound Ratio = 5 : 8
Practice Questions on Ratio Formula
Question 1: Simplify the ratio: 72 : 108
Question 2: Convert the fraction 28/42 into a ratio.
Question 3: Convert the decimal 1.8 into a ratio.
Question 4: Convert 80% into a ratio.
Question 5: If a : b = 4 : 7 and a = 20, find the value of b.
FAQ on Ratio Formula
1. What is the ratio formula with an example?
Ratio Formula = First Quantity / Second Quantity
or
a : b = a/b
For example, if there are 10 boys and 15 girls in a class:
Boys : Girls = 10 : 15 = 2 : 3
2. How do you calculate the ratio quickly in SSC and RRB exams?
To calculate a ratio quickly, first convert both quantities into the same unit and then divide both terms by their Highest Common Factor (HCF).
For example: 45 : 60
HCF = 15
45 : 60 = 3 : 4
This method is widely used in SSC, RRB, Banking, NDA and CDS examinations.
3. How do you convert a percentage into a ratio?
To convert a percentage into a ratio, divide the percentage by 100, simplify the fraction and then write it in ratio form.
For example:
40%
= 40/100
= 2/5
Therefore,
40% = 2 : 5
4. How do you find an unknown value using a ratio formula?
If one quantity and the ratio are known, the unknown quantity can be found using the ratio formula.
For example:
If a : b = 2 : 3 and b = 18
Then,
a/18 = 2/3
3a = 36
a = 12
Therefore, a = 12.
5. Can a ratio be expressed as a fraction?
Yes. A ratio can be expressed as a fraction. For example;
4/5= 4:5
6. Can a ratio be expressed as a decimal?
Yes. We can express a ratio in decimal form. For example;
4:5= 4/5=0.8. Therefore, the ratio 4 : 5 can be expressed as the decimal 0.8.
Related Ratio and Proportion Resources:
- Ratio and Proportion
- Basic Ratio Questions & Answers
- Ratio Word Problems with Answers
- Proportion Questions and Answers with Solutions
- Unitary Method Questions and Answers with Solutions
- Direct Proportion Questions and Answers
- Inverse Proportion Questions & Answers with Solutions
- Ratio and Proportion Practice Questions with Answers
- Ratio and Proportion PYQs SSC, RRB, Banking & Defence Exams (Solved)