What is Ratio Formula?

In mathematics, two or more numbers have been compared by using the term ratio. It is used to express how large or small an amount is in comparison to another. Two numbers are compared using division in a ratio. The dividend is referred to as the ‘antecedent,’ while the divisor is referred to as the ‘consequent.’ For example: In a group of 30, 17 prefer to walk in the morning and 13 prefer to bike. To describe this information as a ratio, we write it as 17: 13. The sign ‘:’ is used as “is to” in this context. As a result, the ratio of persons who prefer walking to those who prefer cycling is ’17 to 13′.

Ratio 

The ratio is defined as a comparison of two quantities of the same unit to determine how much of one quantity is contained in the other. Ratios are divided into two sorts. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between two separate entities or groupings. For example, 

• The boy-to-girl ratio in a class is 12: 15, but the part-to-whole ratio represents the relationship between a specific group and the total. 
• Five people out of every ten enjoy reading. As a result, the part to total ratio is 5: 10, which suggests that 5 out of every 10 persons enjoy reading.

Ratio Formula 

When comparing the connection between two numbers or quantities, we use the ratio formula. The standard manner of describing a ratio of two values say ‘p’ and ‘q,’ is p: q, which may be read as ‘p is to q’. This ratio is represented by the fraction p/q. To simplify a ratio, even more, we utilize the same method we used to simplify a fraction. The steps below can be used to calculate the ratio of the two quantities. 

For example, if we require 20 cups of flour and 30 cups of sugar to make fluffy pancakes, we may compute the flour-to-sugar ratio in the recipe. Here 20 : 30 = 20/30 

Or here “p” i.e 20 is referred to as antecedent and ” q” i.e 30 is referred as consequent. 

• Step 1: Determine the quantities for both cases for which we are calculating the ratio. In this example, It is 20 and 30.
• Step 2: Write it as a fraction p/q. As a result, we write it as 20/30.
• Step 3: If necessary, simplify the fraction even more. we will get the final ratio after simplification. In this case, 20/30 may be simplified to 2/3.
• Step 4: As a result, the flour-to-sugar ratio can be expressed as 2 : 3.

p:q = p/q 

Here “p” is referred as antecedent and ” q” is referred as consequent.

Sample Questions

Question 1:  In a class of 100 students, 35 are girls and the remaining are boys. By Using the ratio formula, find the ratio of the number of boys to the number of girls.

Solution:

To find the Ratio of the number of boys to the number of girls,

Given: Total number of students = 100

Number of girls = 35

Number of boys = Total number of students – Number of girls

= 100 – 35

= 65 

Using ratio formula,

The ratio of number of boys to the number of girls = Number of boys: Number of girls 

= 65 : 35 

Question 2: The ratio of p and q is 7: 5 . If p = 35, what is the value of q?

Solution: 

To find: Value of q

Given: Ratio of p to q = 7 : 5

Using ratio formula,

p : q = 7 : 5

p/q  = 7/5

35/q = 7/5

q = (5/7) × 35

q = 175 / 7

q = 25

So the value of q is 25.

Question 3: If p:q = 4 : 5 , find the ratio 4p + 5q : 5p + 6q?

Solution:

Given: p : q = 4 : 5 

We can write it above equation as,

p/q = 4/5 

p = 4/5 q

To find the ratio, 4p + 5q : 5p + 6q

By substituting the value of p in equation, 4p + 5q : 5p + 6q

= 4(4q/5) + 5q :  5 (4q/5) + 6q 

= 16q/5 + 5 q :  4q + 6q

= (16q + 25q)/5 :  10 q 

= 41q / 5 : 10 q 

By simplifying, the ratio will be 41q : 50q

Therefore, the ratio 4p + 5q : 5p + 6q is 41:50.

Question 4:  The ratio of p and q is 6 : 3 . If p = 20, what is the value of q?

Solution:

To find: Value of q

Given: Ratio of p to q = 6 : 3

Using ratio formula,

 p : q = 6 : 3

 p/q  = 6/3

20/q = 6/3

q = (3/6) × 20

q = 60/6

q = 10

So the value of q is 10.

Question 5: Two numbers are in ratio 2: 6, if 6 is added to each number, then the ratio becomes 3: 5? Find the numbers?

Solution:

Let the required numbers be 2x and 6x 

given that if 6 is added to each number then the ratio becomes 3 : 5 

i.e; 2x + 6 : 6x + 6 = 3 : 5

(2x + 6 )/ (6x + 6) = 3/5

(2x + 6 )5  = (6x + 6)3

10x + 30 = 18x + 18 

30 – 18  =  18x – 10x 

12 =  8x

x = 12/8 

Therefore the numbers are 2x = 2 × 12/8 

= 24/8

= 3 

6x = 6 × 12/8

= 72/8

= 9

So the numbers are 3 and 9. 

Question 6: The ratio of income to the expenditure of a family is 6: 5 . Find the savings if the income is Rs 12000?

Solution:

Given income: Rs 12000

Given that ratio of income and expenditure = 6 : 5 

Therefore 6x = 12000

x = 12000/6

= 2000

Expenditure = 5x = 5 x 2000

= 10000 

Therefore the savings will be, income – expenditure 

= 12000 – 10000

= Rs 2000

Question 7: Two numbers are in ratio 4: 5, if 9 is subtracted from each number, then the ratio becomes 7: 8? Find the numbers?

Solution: 

Let the required numbers be 4x and 5x

given that if 9 is subtracted from each number then the ratio becomes 7 : 8

i.e; 4x -9 : 5x – 9 = 7 : 8

(4x – 9)/ (5x – 9) = 7/8

(4x – 9)8  =  (5x – 9)7

32x – 72 = 35x – 63

32x – 35x  =  -63 + 72

-3x =  9

x = -3

Therefore the numbers are 4x = 4 × -3 = -12

5x = 5 × -3 = -15

So the numbers are -12 and -15.