426. If 5.5 of a = 0.65 of b, then a : b is equal to :

1. 1. 13 : 11

   
   
   

   2. 11 : 13

   
   
   

   3. 13 : 110

   
   
   

   4. 110 : 13

   
   
   

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1. View Hint View Answer Discuss in Forum

   a × 5.5 = b × 0.65
   

   ⇒	a	=	0.65	=	65	=	13
   	b		5.5		550		110

   Correct Option: C

   a × 5.5 = b × 0.65
   

   ⇒	a	=	0.65	=	65	=	13
   	b		5.5		550		110

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427. The ratio of boys and girls in a college is 5 : 3. If 50 boys leave the college and 50 girls join the college, the ratio becomes 9 : 7. The number of boys in the college is

1. 1. 300

   
   
   

   2. 400

   
   
   

   3. 500

   
   
   

   4. 600

   
   
   

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1. View Hint View Answer Discuss in Forum

   Original number of boys = 5x
   Original number of girls = 3x
   

   ∴	5x − 50	=	9
   	3x + 50		7

   
   ⇒  35x – 350 = 27x + 450
   ⇒  35x – 27x = 350 + 450
   ⇒  8x = 800
   ⇒  x = 100
   Number of boys = 5x
   = 5 × 100 = 500

   Correct Option: C

   Original number of boys = 5x
   Original number of girls = 3x
   

   ∴	5x − 50	=	9
   	3x + 50		7

   
   ⇒  35x – 350 = 27x + 450
   ⇒  35x – 27x = 350 + 450
   ⇒  8x = 800
   ⇒  x = 100
   Number of boys = 5x
   = 5 × 100 = 500

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428. If A =	2	of B and B =	4	of C, then A : B : C is.
     	3		5

1. 1. 12 : 8 : 10

   
   
   

   2. 15 : 10 : 8

   
   
   

   3. 10 : 15 : 12

   
   
   

   4. 8 : 12 : 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   A = B ×	2
   	3

   
   ⇒  A : B = 2 : 3 = 8 : 12
   

   B = C ×	4
   	5

   
   ⇒  B : C = 4 : 5 = 12 : 15
   Second Method :
   Here, A : B = 2 : 3, B : C = 4 : 5
   A : B : C= xp : yp : qy
   = 2 × 4 : 3 × 4 : 5× 3
   = 8 : 12 : 15

   Correct Option: D

   A = B ×	2
   	3

   
   ⇒  A : B = 2 : 3 = 8 : 12
   

   B = C ×	4
   	5

   
   ⇒  B : C = 4 : 5 = 12 : 15
   Second Method :
   Here, A : B = 2 : 3, B : C = 4 : 5
   A : B : C= xp : yp : qy
   = 2 × 4 : 3 × 4 : 5× 3
   = 8 : 12 : 15

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429. To get the ratio p : q (for p ≠ q), one has to add a number to each term of the ratio x : y, the number is

1. 1. px + qy

      p − q

   
   
   

   2. qx − py

      p − q

   
   
   

   3. px − qy

      p − q

   
   
   

   4. py − qx

      p − q

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number to be added be z.
   

   ∴	x + z	=	p
   	y + z		q

   
   ⇒  qx + zq = py + zp
   ⇒  zp – zq = qx – py
   ⇒  z (p – q) = qx – py
   

   ⇒  z =	qx − py
   	p − q

   Correct Option: B

   Let the number to be added be z.
   

   ∴	x + z	=	p
   	y + z		q

   
   ⇒  qx + zq = py + zp
   ⇒  zp – zq = qx – py
   ⇒  z (p – q) = qx – py
   

   ⇒  z =	qx − py
   	p − q

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430. The third proportional of 12 and 18 is

1. 1. 3

   
   
   

   2. 6

   
   
   

   3. 27

   
   
   

   4. 144

   
   
   

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1. View Hint View Answer Discuss in Forum

   Third proportional of 12 and 18 = x
   ∴  12 : 18 = 18 : x
   

   ⇒  x =	18 × 18	= 27
   	12

   
   Second Method :
   

   Third proportion =	b2	=	182
   	a		12

   
   

   =	18 × 18	= 27
   	12

   Correct Option: C

   Third proportional of 12 and 18 = x
   ∴  12 : 18 = 18 : x
   

   ⇒  x =	18 × 18	= 27
   	12

   
   Second Method :
   

   Third proportion =	b2	=	182
   	a		12

   
   

   =	18 × 18	= 27
   	12

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