376. If b is the mean proportional of a and c, then (a – b)³ : (b – c)³ equals

1. 1. a³ : c³

   
   
   

   2. b² : c²

   
   
   

   3. a² : c²

   
   
   

   4. a³ : b³

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since b is the mean proportional of a and c.
   

   ∴	a	=	b	= k (Suppose)
   	b		c

   
   ∴  a = bk, b = ck
   

   ∴	(a − b)3	=	(bk − b)3
   	(b − c)3		(ck − c)3

   
   

   =	b3(k − 1 )3	=	b3	=	a3
   	c3(k − 1 )3		c3		b3

   Correct Option: D

   Since b is the mean proportional of a and c.
   

   ∴	a	=	b	= k (Suppose)
   	b		c

   
   ∴  a = bk, b = ck
   

   ∴	(a − b)3	=	(bk − b)3
   	(b − c)3		(ck − c)3

   
   

   =	b3(k − 1 )3	=	b3	=	a3
   	c3(k − 1 )3		c3		b3

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377. ₹ 6200 divided into three parts proportional to
     

     1	:	1	:	1
     2		3		5

     are respectively

1. 1. ₹ 3000, ₹ 2000, ₹ 1200

   
   
   

   2. ₹ 3500, ₹ 1500, ₹ 1200

   
   
   

   3. ₹ 2500, ₹ 2000, ₹ 1700

   
   
   

   4. ₹ 2200, ₹ 3000, ₹ 1000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Ratio =	1	:	1	:	1
   	2		3		5

   
   

   =	1	× 30 :	1	× 30 :	1	× 30 = 15 : 10 : 6
   	2		3		5

   
   Sum of the ratios
   = 15 + 10 + 6 = 31
   

   ∴  First part = ₹	15	× 6200
   	31

   
   = ₹ 3000
   

   Second part = = ₹.	10	× 6200
   	31

   
   = ₹ 2000
   

   Third part = = ₹	6	× 6200
   	31

   
   = ₹ 1200

   Correct Option: A

   Ratio =	1	:	1	:	1
   	2		3		5

   
   

   =	1	× 30 :	1	× 30 :	1	× 30 = 15 : 10 : 6
   	2		3		5

   
   Sum of the ratios
   = 15 + 10 + 6 = 31
   

   ∴  First part = ₹	15	× 6200
   	31

   
   = ₹ 3000
   

   Second part = = ₹.	10	× 6200
   	31

   
   = ₹ 2000
   

   Third part = = ₹	6	× 6200
   	31

   
   = ₹ 1200

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378. 94 is divided into two parts in such a way that the fifth part of the first and the eighth part
     of the second are in the ratio 3 : 4. The first part is :

1. 1. 30

   
   
   

   2. 36

   
   
   

   3. 40

   
   
   

   4. 28

   
   
   

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1. View Hint View Answer Discuss in Forum

   First part = x and second part
   = 94 – x

   ∴	x
   	5
   	94 − x
   	8

   
   

   ∴	x			= 3/4
   	5
   	94 − x
   	8

   
   

   ⇒	x	×	8	=	3
   	5		(94 − x)		4

   
   ⇒  32 x = 15 × 94 – 15x
   ⇒  47 x = 15 × 94
   

   ⇒  x =	15 × 94	= 30
   	47

   Correct Option: A

   First part = x and second part
   = 94 – x

   ∴	x
   	5
   	94 − x
   	8

   
   

   ∴	x			= 3/4
   	5
   	94 − x
   	8

   
   

   ⇒	x	×	8	=	3
   	5		(94 − x)		4

   
   ⇒  32 x = 15 × 94 – 15x
   ⇒  47 x = 15 × 94
   

   ⇒  x =	15 × 94	= 30
   	47

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379. If a : b = 5 : 7 and c : d = 2a : 3b, then ac : bd is :

1. 1. 20 : 38

   
   
   

   2. 50 : 147

   
   
   

   3. 10 : 21

   
   
   

   4. 50 : 151

   
   
   

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1. View Hint View Answer Discuss in Forum

   a	=	5	,	c	=	2a
   b		7		d		3b

   
   

   ⇒	a	×	c	=	5	×	2a
   	b		d		7		3b

   
   

   ⇒	ac	=	10	×	5	=	50
   	bd		21		7		147

   Correct Option: B

   a	=	5	,	c	=	2a
   b		7		d		3b

   
   

   ⇒	a	×	c	=	5	×	2a
   	b		d		7		3b

   
   

   ⇒	ac	=	10	×	5	=	50
   	bd		21		7		147

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380. If x : y = 3 : 2, then the ratio 2x² + 3y² : 3x² – 2y² is equal to :

1. 1. 12 : 5

   
   
   

   2. 6 : 5

   
   
   

   3. 30 : 19

   
   
   

   4. 5 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x : y = 3 : 2
   ⇒  x² : y² = 9 : 4
   

   ∴	2x2 + 3y2
   	3x2 − 2y2

   
   

   =	2	x2	+ 3
   		y2
   	3	x2	− 2
   		y2

   
   

   =	2 ×	9	+ 3
   		4
   	3 ×	9	− 2
   		4

   
   
   

   =	18 + 2
   	4
   	27 − 8
   	4

   
   = 30 : 19

   Correct Option: C

   x : y = 3 : 2
   ⇒  x² : y² = 9 : 4
   

   ∴	2x2 + 3y2
   	3x2 − 2y2

   
   

   =	2	x2	+ 3
   		y2
   	3	x2	− 2
   		y2

   
   

   =	2 ×	9	+ 3
   		4
   	3 ×	9	− 2
   		4

   
   
   

   =	18 + 2
   	4
   	27 − 8
   	4

   
   = 30 : 19

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