# WRITE THE RATIO

Write the ratio :

Here we are going to see how to write the ratio of two quantities.

What is ratio ?

Ratio is a way to compare two or more quantities of the same kind. The ratio of two non-zero quantities a and b is written as a : b. It is read as “a is to b”

When two quantities a and b are compared they must be in the same unit .

For example: If a = 1 m 20 cm and b = 90 cm then a must be written as 120 cm and b = 90 cm and the ratio a : b is 120 : 90

Let us see some example problems based on the above concept.

Example 1 :

In a Village of 10,000 people, 4,000 are Government Employees and the remaining are self-employed. Find the ratio of

(i) Government employees to people of the village.

(ii) Self employed to people of the village.

(iii) Government employees to self-employed.

Solution :

Number of people in the village  =  10,000

Number of Government employees  =  4,000

Self employed = 10,000 – 4,000  =  6,000

Government employees to people of the village

=  4000 : 6000

In order to simplify the ratio, we can write it in fractional form, that is

4000/6000  =  4/6  =  3/2 ==>  3 : 2

(ii) Government employees to people of the village

=  6000 : 10000

In order to simplify the ratio, we can write it in fractional form, that is

6000/10000  =  6/10  =  3/5 ==>  3 : 5

(iii) Government employees to self employed.

=  4000 : 6000

In order to simplify the ratio, we can write it in fractional form, that is

4000/6000  =  4/6  =  2/3 ==>  2 : 3

Example 2 :

John is 50 years old, his son is 10 years old. Write down the ratio between their ages.

(i) 5 years ago (ii) At present (iii) After 5 years

Solution :

Age of John  =  50 years

Age of his son  =  10 years

(i) 5 years ago,  the ratio of ages between John to his son

=   (50 - 5)  :  (10 - 5)

=  45 : 5

=  9 : 1

(ii) at present,  the ratio of ages between John to his son

=   50  :  10

=  5 : 1

(iii) After 5 years,  the ratio of ages between John to his son

=   (50 + 5)  :  (10 + 5)

=  55 : 15

=  55/15   =  11/3

=  11 : 3

Example 3 :

What is the ratio of stars to circles?

Solution :

Number of stars   =  3

Number of circles  =  4

Hence the ratio between the number of stars to the number of circles is  3 : 4

Example 4 :

What is the ratio of circles to total shapes?

Solution :

Number of circles  =  7

Number of shapes  =  8

Hence the ratio between the number of circles to the total shapes is  7 : 8

Example 5 :

Write the ratio of the following

1kg to 500g

Solution :

Since the given two quantities are not in same kind, we have to convert kg into grams.

1000 grams  =  1 kg

ratio between two quantities

1000 grams  :  500 grams

1000/500  =  2/1  =  2 : 1

Hence the ratio between the given two quantities are 2 : 1

After having gone through the stuff given above, we hope that the students would have understood "Write an equivalent ratio".

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