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

1. 1. 3 : 7

   
   
   

   2. 7 : 3

   
   
   

   3. 21 : 10

   
   
   

   4. 10 : 21

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

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

1. 1. 4 : 9

   
   
   

   2. 9 : 4

   
   
   

   3. 11 : 1

   
   
   

   4. 9 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

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3. The ratio 2^1.5 : 2^0.5 is the same as :

1. 1. 2 : 1

   
   
   

   2. 3 : 1

   
   
   

   3. 6 : 1

   
   
   

   4. 3 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

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

1. 1. 8.9

   
   
   

   2. 56

   
   
   

   3. 14

   
   
   

   4. 17

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

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

1. 1. 13 : 14

   
   
   

   2. 14 : 13

   
   
   

   3. 10 : 11

   
   
   

   4. 11 : 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

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