**Write an equivalent ratio : **

We can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.

**Example 1 :**

Give two equivalent ratios of 6 : 4

**Solution :**

In order to find equivalent ratio, we have to multiply the numerator and denominator by the same number.

6 : 4 = 6/4

Multiplying the numerator and denominator by 2, we get

(6/4) x (2/2) = 12/8 = 12 : 8

Multiplying the numerator and denominator by 3, we get

(6/4) x (3/3) = 18/12 = 18 : 12

Hence the equivalent ratios of 6 : 4 are 12 : 8 and 18 : 12.

**Example 2 :**

Ratio of distance of the school from Mary’s home to the distance of the school from John’s home is 2 : 1.

(a) Who lives nearer to the school?

(b) Complete the following table which shows some possible distances that Mary and John could live from the school.

Distance from Mary’s home to school (in km.) |
10 |
? |
4 |
? |
? |

Distance from John’s home to school (in km.) |
5 |
4 |
? |
3 |
1 |

(c) If the ratio of distance of Mary’s home to the distance of Kalam’s home from school is 1 : 2, then who lives nearer to the school?

**Solution :**

(a) Let **2x ** and **1x **be the **d****istance from Mary’s home to school** and the **d****istance from John’s home to school **respectively.

From the given ratio, we come to know that John lives nearer to school.

(b) let a, b, c and d are missing numbers respectively.

From the given information, we come to know that the distance from Mary's home to school and "John's home to the school is in the ratio 2 : 1 (equivalent ratio)

**Value of a :**

10 : 5 = a : 4

10 (4) = a(5)

a = 10 (4)/5 ==> 40/5 ==> 8

**Value of b :**

10 : 5 = 4 : b

10 b = 5(4)

b = 5(4)/10 ==> 20/10 ==> 2

**Value of c :**

10 : 5 = c : 3

10 (3) = 5 c

c = 30/5 ==> 6

**Value of d :**

10 : 5 = d : 1

10 (1) = 5 d

d = 10/5 ==> 2

Distance from Mary’s home to school (in km.) |
10 |
8 |
4 |
6 |
2 |

Distance from John’s home to school (in km.) |
5 |
4 |
2 |
3 |
1 |

(c) Since the ratio is 1 : 2, so Mary lives nearer to the school.

**Example 3 :**

Present age of father is 42 years and that of his son is 14

years. Find the ratio of

(a) Present age of father to the present age of son.

(b) Age of the father to the age of son, when son was 12 years old.

(c) Age of father after 10 years to the age of son after 10 years.

(d) Age of father to the age of son when father was 30 years old.

**Solution :**

(a) Present age of father to the present age of son.

Present age of father = 42

Present age of son = 14

Ratio between father's age and son's age = 42 : 14

(42 ÷ 7)/(14 ÷ 7) ==> 6/2 ==> 3 : 1

(b) Age of the father to the age of son, when son was 12 years old.

Two years ago age of father = 42 - 2 ==> 40

Two years ago age of son = 14 - 2 ==> 12

40 : 12 ==> 20 : 6 ==> 10 : 3

(c) Age of father after 10 years to the age of son after 10 years.

Ten years after father's age = 42 + 10 ==> 52

Ten years after son's age = 14 + 10 ==> 24

52 : 24 ==> 26 : 12 ==> 13 : 6

(d) Age of father to the age of son when father was 30 years old.

12 years ago :

father's age = 42 - 12 ==> 30

son's age = 14 - 12 ==> 2

30 : 2 ==> 15 : 1

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