536. There is a ratio of 5 : 4 between two numbers. If 40 per cent of the first is 12, then 50% of the
     second number is

1. 1. 12

   
   
   

   2. 24

   
   
   

   3. 18

   
   
   

   4. 20

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let numbers = 5x and 4x
   

   ∴  5x ×	40	= 12
   	100

   
   ⇒  2x = 12 ⇒ x = 6 and
   Second number = 6 × 4 = 24
   

   ∴  50% of 24 = 24 ×	50	= 12
   	100

   Correct Option: A

   Let numbers = 5x and 4x
   

   ∴  5x ×	40	= 12
   	100

   
   ⇒  2x = 12 ⇒ x = 6 and
   Second number = 6 × 4 = 24
   

   ∴  50% of 24 = 24 ×	50	= 12
   	100

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537. The reciprocals of the squares of the numbers

     1	1	and 1	1	. are in the ratio
     	2		3

1. 1. 64 : 81

   
   
   

   2. 8 : 9

   
   
   

   3. 81 : 64

   
   
   

   4. 9 : 85

   
   
   

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1. View Hint View Answer Discuss in Forum

   Ratio of the squares of	3	and	4
   	2		3

   
   

   =	9	:	16
   	4		9

   
   Ratio of their reciprocals
   

   =	4	:	9
   	9		16

   
   = 64 : 81

   Correct Option: A

   Ratio of the squares of	3	and	4
   	2		3

   
   

   =	9	:	16
   	4		9

   
   Ratio of their reciprocals
   

   =	4	:	9
   	9		16

   
   = 64 : 81

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538. Rs. 782 is divided into three parts in the ratio

     1	:	2	:	3	, the first part is
     2		3		4

1. 1. Rs. 182

   
   
   

   2. Rs. 204

   
   
   

   3. Rs. 190

   
   
   

   4. Rs. 196

   
   
   

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1. View Hint View Answer Discuss in Forum

   A : B : C =	1	:	2	:	3
   	2		3		4

   
   

   =		1	× 12		:		2	× 12		:		3	× 12
   		2					3					4

   
   = 6 : 8 : 9
   Sum of the terms of ratio
   = 6 + 8 + 9 = 23
   ∴  First part
   

   = Rs.		6	× 782		= Rs. 204
   		23

   Correct Option: B

   A : B : C =	1	:	2	:	3
   	2		3		4

   
   

   =		1	× 12		:		2	× 12		:		3	× 12
   		2					3					4

   
   = 6 : 8 : 9
   Sum of the terms of ratio
   = 6 + 8 + 9 = 23
   ∴  First part
   

   = Rs.		6	× 782		= Rs. 204
   		23

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539. Find the fraction which bears the same ratio to 1/27 that 3/27 does to 5/9.

1. 1. 5

      9

   
   
   

   2. 1

      35

   
   
   

   3. 45

      7

   
   
   

   4. 7

      45

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the required fraction be x.
   According to the question,
   

   <

   x :	1	=	3	:	5
   	27		7		9

   
   

   ⇒  x ×	5	=	1	×	3	=	1
   	9		27		7		63

   
   

   ⇒  x =	1	×	9	=	1
   	63		5		35

   Correct Option: B

   Let the required fraction be x.
   According to the question,
   

   <

   x :	1	=	3	:	5
   	27		7		9

   
   

   ⇒  x ×	5	=	1	×	3	=	1
   	9		27		7		63

   
   

   ⇒  x =	1	×	9	=	1
   	63		5		35

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540. A and B together have Rs. 6300. If	5	th of
     	27

     
     

     A’s amount is equal to	2	th of B’s amount.
     	5

     The amount of ‘B’ is

1. 1. Rs. 2500

   
   
   

   2. Rs. 3800

   
   
   

   3. Rs. 2300

   
   
   

   4. Rs. 4000

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   

   5A	=	2B
   19		5

   
   

   ⇒  5A =	19 × 2B
   	5

   
   

   ⇒  A =	38 × B
   	5 × 5

   
   ⇒  A : B = 38 : 25
   Sum of the terms of ratio
   = 38 + 25 = 63
   

   ⇒  B’s share = Rs.		25	× 6300
   		63

   
   = Rs. 2500

   Correct Option: A

   According to the question,
   

   5A	=	2B
   19		5

   
   

   ⇒  5A =	19 × 2B
   	5

   
   

   ⇒  A =	38 × B
   	5 × 5

   
   ⇒  A : B = 38 : 25
   Sum of the terms of ratio
   = 38 + 25 = 63
   

   ⇒  B’s share = Rs.		25	× 6300
   		63

   
   = Rs. 2500

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