501. Four numbers are in the ratio 1 : 2 : 3 : 4. Their sum is 16. The sum of the first and fourth
     number is equal to :

1. 1. 5

   
   
   

   2. 8

   
   
   

   3. 10

   
   
   

   4. 80

   
   
   

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1. View Hint View Answer Discuss in Forum

   x + 2x + 3x + 4x = 16
   

   ∴  x =	16	= 1.6
   	10

   
   ∴  Sum = 1.6 + 6.4 = 8

   Correct Option: B

   x + 2x + 3x + 4x = 16
   

   ∴  x =	16	= 1.6
   	10

   
   ∴  Sum = 1.6 + 6.4 = 8

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502. The ratio of two numbers is 3 : 8 and their difference is 115. The smaller of the two numbers is :

1. 1. 184

   
   
   

   2. 194

   
   
   

   3. 69

   
   
   

   4. 59

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 3x and 8x.
   ∴  8x – 3x = 115
   

   ⇒  5x = 115 ⇒ x =	115	= 23
   	5

   
   ∴  The smaller number
   = 3x = 3 × 23 = 69

   Correct Option: C

   Let the numbers be 3x and 8x.
   ∴  8x – 3x = 115
   

   ⇒  5x = 115 ⇒ x =	115	= 23
   	5

   
   ∴  The smaller number
   = 3x = 3 × 23 = 69

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503. The present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively :

1. 1. 18 years, 27 years

   
   
   

   2. 21 years, 28 years

   
   
   

   3. 24 years, 32 years

   
   
   

   4. 27 years, 36 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   A’s present age = 3x years (let)
   B’s present age = 4x years
   According to the question,
   10 years ago,
   

   3x − 10	=	4
   4x − 10		7

   
   ⇒  21x – 70 = 16x – 40
   ⇒  21x – 16x = 70 – 40
   ⇒  5x = 30
   

   ⇒  x =	30	= 6
   	5

   
   ∴  A’s present age
   = 3x = 3x × 6 = 18 years
   B’s present age
   = 4x = 4 × 6 = 24 years

   Correct Option: A

   A’s present age = 3x years (let)
   B’s present age = 4x years
   According to the question,
   10 years ago,
   

   3x − 10	=	4
   4x − 10		7

   
   ⇒  21x – 70 = 16x – 40
   ⇒  21x – 16x = 70 – 40
   ⇒  5x = 30
   

   ⇒  x =	30	= 6
   	5

   
   ∴  A’s present age
   = 3x = 3x × 6 = 18 years
   B’s present age
   = 4x = 4 × 6 = 24 years

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504. The ratio of A’s age to B’s age is 4 : 3. ‘A’ will be 26 years old after 6 years. The age of B now is :

1. 1. 19	1	years
      	2

   
   
   

   2. 12 years

   
   
   

   3. 21 years

   
   
   

   4. 15 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   A’s present age
   = 4x years (let).
   According to the question,
   4x + 6 = 26
   ⇒  4x = 26 – 6 = 20
   

   ⇒  x =	20	= 5
   	4

   
   ∴  B’s present age = 3x = 3 × 5
   = 15 years

   Correct Option: D

   A’s present age
   = 4x years (let).
   According to the question,
   4x + 6 = 26
   ⇒  4x = 26 – 6 = 20
   

   ⇒  x =	20	= 5
   	4

   
   ∴  B’s present age = 3x = 3 × 5
   = 15 years

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505. The ratio of the present ages of two boys is 3:4. After 3 years, the ratio of their ages is equal to will be 4:5.The ratio of their ages after 21 years will be

1. 1. 14:17

   
   
   

   2. 17:19

   
   
   

   3. 11:12

   
   
   

   4. 10:11

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the ages of boys be 3x and 4x years respectively.
   According to the question,
   After 3 years
   

   3x + 3	=	4
   4x + 3		5

   
   ⇒  16x + 12 = 15x + 15
   ⇒  16x – 15x = 15 – 12
   ⇒  x = 3
   

   ∴  Required ratio after 21 years =	3x + 21
   	4x + 21

   
   

   3 × 3 + 21	=	9 + 21
   4 × 3 + 21		12 + 21

   
   

   30	=	10
   33		11

   Correct Option: D

   Let the ages of boys be 3x and 4x years respectively.
   According to the question,
   After 3 years
   

   3x + 3	=	4
   4x + 3		5

   
   ⇒  16x + 12 = 15x + 15
   ⇒  16x – 15x = 15 – 12
   ⇒  x = 3
   

   ∴  Required ratio after 21 years =	3x + 21
   	4x + 21

   
   

   3 × 3 + 21	=	9 + 21
   4 × 3 + 21		12 + 21

   
   

   30	=	10
   33		11

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