**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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