481. Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional ?

1. 1. 6

   
   
   

   2. 5

   
   
   

   3. 4

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let required number be x.
   

   ∴	6 + x	=	15 + x
   	7 + x		17 + x

   
   ⇒  102 + 17x + 6x + x²
   = 105 + 7x + 15x + x²
   ⇒  23x – 22x = 105 – 102
   ⇒  x = 3
   Note : It is convenient to solve it orally using options
   

   6 + 3	=	15 + 3	⇒	9	=	18
   7 + 3		17 + 3		10		20

   
   Second Method :
   

   Required Number =	bc − ad
   	(a + d) − (b + c)

   
   Where a = 6, b = 7, c = 15, d = 17
   

   =	7 × 15 − 6 × 17
   	(6 + 17) − (7 + 15)

   
   

   =	105 − 102	= 3
   	23 − 22

   Correct Option: D

   Let required number be x.
   

   ∴	6 + x	=	15 + x
   	7 + x		17 + x

   
   ⇒  102 + 17x + 6x + x²
   = 105 + 7x + 15x + x²
   ⇒  23x – 22x = 105 – 102
   ⇒  x = 3
   Note : It is convenient to solve it orally using options
   

   6 + 3	=	15 + 3	⇒	9	=	18
   7 + 3		17 + 3		10		20

   
   Second Method :
   

   Required Number =	bc − ad
   	(a + d) − (b + c)

   
   Where a = 6, b = 7, c = 15, d = 17
   

   =	7 × 15 − 6 × 17
   	(6 + 17) − (7 + 15)

   
   

   =	105 − 102	= 3
   	23 − 22

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482. Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is

1. 1. 20

   
   
   

   2. 27

   
   
   

   3. 39

   
   
   

   4. 52

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 3x, 4x and 5x.
   ∴  5x + 3x = 4x + 52
   ⇒  4x = 52 ⇒ x =13
   ∴  The smallest number
   = 3x = 3 × 13 = 39

   Correct Option: C

   Let the numbers be 3x, 4x and 5x.
   ∴  5x + 3x = 4x + 52
   ⇒  4x = 52 ⇒ x =13
   ∴  The smallest number
   = 3x = 3 × 13 = 39

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483. If the sum of two quantities is equal to three times their difference, then the ratio of the two
     quantities is

1. 1. 1 : 3

   
   
   

   2. 3 : 1

   
   
   

   3. 2 : 1

   
   
   

   4. 2 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x + y = 3 (x – y)
   ⇒  x + y = 3x – 3y Þ 2x = 4y
   

   ⇒	x	=	2	⇒ x : y = 2 : 1
   	y		1

   Correct Option: C

   x + y = 3 (x – y)
   ⇒  x + y = 3x – 3y Þ 2x = 4y
   

   ⇒	x	=	2	⇒ x : y = 2 : 1
   	y		1

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484. Two numbers are in the ratio 1 : 3. If their sum is 240, then their difference is

1. 1. 120

   
   
   

   2. 108

   
   
   

   3. 100

   
   
   

   4. 96

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 3x and x,
   Then, 3x + x = 240
   ⇒  4x = 240
   

   ⇒  x =	240	= 60
   	4

   
   ∴  Difference = 3x – x = 2x
   = 2 × 60 = 120

   Correct Option: A

   Let the numbers be 3x and x,
   Then, 3x + x = 240
   ⇒  4x = 240
   

   ⇒  x =	240	= 60
   	4

   
   ∴  Difference = 3x – x = 2x
   = 2 × 60 = 120

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485. Three numbers are in the ratio 5 : 6 : 7. If the product of the numbers is 5670, then the greatest number is

1. 1. 15

   
   
   

   2. 18

   
   
   

   3. 21

   
   
   

   4. 28

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 5x, 6x and 7x respectively.
   ∴  5x × 6x × 7x = 5670
   

   ⇒  x3 =	5670	= 27
   	5 × 6 × 7

   
   ∴  x³ = √27 = 3
   ∴  The greatest number = 7x
   = 7 × 3 = 21

   Correct Option: C

   Let the numbers be 5x, 6x and 7x respectively.
   ∴  5x × 6x × 7x = 5670
   

   ⇒  x3 =	5670	= 27
   	5 × 6 × 7

   
   ∴  x³ = √27 = 3
   ∴  The greatest number = 7x
   = 7 × 3 = 21

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