## Ratio, Proportion

#### Ratio, Proportion

1. If A : B = 3 : 4, B : C = 5 : 7 and C : D = 8 : 9 then A : D is equal to

1.  A : D = A = A × B × C D B C D

 = 3 × 5 × 8 = 10 = 10 : 21 4 7 9 21

Second Method :
A : D = xpm : yqn
= 3 × 5 × 8 : 4 × 7 × 9
= 10 : 21

##### Correct Option: D

 A : D = A = A × B × C D B C D

 = 3 × 5 × 8 = 10 = 10 : 21 4 7 9 21

Second Method :
A : D = xpm : yqn
= 3 × 5 × 8 : 4 × 7 × 9
= 10 : 21

1. If m : n = 3 : 2, then (4m + 5n) : (4m – 5n) is equal to :

1.  m = 3 (Given) n 2

 ∴ 4m + 5n 4m − 5n
 = 4 m + 5 n 4 5 − 5 2

 = 4 × 3 + 5 2 4 × 3 − 5 2

 = 6 + 5 = 11 : 1 6 − 5

##### Correct Option: C

 m = 3 (Given) n 2

 ∴ 4m + 5n 4m − 5n
 = 4 m + 5 n 4 5 − 5 2

 = 4 × 3 + 5 2 4 × 3 − 5 2

 = 6 + 5 = 11 : 1 6 − 5

1. The ratio 21.5 : 20.5 is the same as :

1.  Required ratio = 21.5 20.5

 = 21.5 − 0.5 1

 2 = 2 : 1 1

##### Correct Option: A

 Required ratio = 21.5 20.5

 = 21.5 − 0.5 1

 2 = 2 : 1 1

1. The fourth proportional to 0.12, 0.21, 8 is :

1. Let the fourth proportional be x

 Then, 0.12 = 8 0.21 x

 or   x = 8 × 0.21 0.12

 or   x = 8 × 21 12

or   x = 14
Second Method :
 Fourth proportion = bc a

 = 0.21 × 18 = 14 0.12

##### Correct Option: C

Let the fourth proportional be x

 Then, 0.12 = 8 0.21 x

 or   x = 8 × 0.21 0.12

 or   x = 8 × 21 12

or   x = 14
Second Method :
 Fourth proportion = bc a

 = 0.21 × 18 = 14 0.12

1. If x : y = 3 : 1, then x3 – y3 : x3 + y3 = ?

1.  x = 3 ⇒ x3 = 27 y 1 y3 1

 ⇒ x3 − y3 = 27 − 1 x3 − y3 27 + 1

[By componendo and dividendo]
 = 26 = 13 = 13 : 14 28 14

##### Correct Option: A

 x = 3 ⇒ x3 = 27 y 1 y3 1

 ⇒ x3 − y3 = 27 − 1 x3 − y3 27 + 1

[By componendo and dividendo]
 = 26 = 13 = 13 : 14 28 14