411. The compound ratio of the inverse ratios of the ratios x : yz, y : zx, z : xy is :

1. 1. 1 : xyz

   
   
   

   2. xyz : 1

   
   
   

   3. 1 : 1

   
   
   

   4. x : yz

   
   
   

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1. View Hint View Answer Discuss in Forum

   Reciprocal ratio
   

   =	yz	:	zx	:	xy
   	x		y		z

   
   Their compound ratio
   

   =	yz.zx.xy	= xyz : 1
   	xyz

   Correct Option: B

   Reciprocal ratio
   

   =	yz	:	zx	:	xy
   	x		y		z

   
   Their compound ratio
   

   =	yz.zx.xy	= xyz : 1
   	xyz

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412. If		x +	1		:		x −	1		= 5 : 3,
     			x					x

     then the value(s) of x is/are

1. 1. ±1

   
   
   

   2. ±2

   
   
   

   3. ±3

   
   
   

   4. 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   

   x +	1			= 5/3
   	x
   x −	1
   	x

   
   

   ⇒ 5x −	5	= 3x +	3
   	x		x

   
   

   ⇒ 5x − 3x =	5	+	3
   	x		x

   
   

   ⇒  2x =	8
   	x

   
   

   ⇒  x2 =	8	= 4
   	2

   
   ⇒  x = √4 = ± 2

   Correct Option: B

   According to the question,
   

   x +	1			= 5/3
   	x
   x −	1
   	x

   
   

   ⇒ 5x −	5	= 3x +	3
   	x		x

   
   

   ⇒ 5x − 3x =	5	+	3
   	x		x

   
   

   ⇒  2x =	8
   	x

   
   

   ⇒  x2 =	8	= 4
   	2

   
   ⇒  x = √4 = ± 2

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413. If the three numbers in the ratio 3 : 2 : 5 be such that the sum of the squares is equal to 1862 then which number is the middle one ?

1. 1. 16

   
   
   

   2. 14

   
   
   

   3. 13

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 3x, 2x and 5x.
   According to the question,
   (3x)² + (2x)² + (5x)² = 1862
   ⇒  9x² + 4x² + 25x² = 1862
   ⇒  38x² = 1862
   

   ⇒  x2 =	1862	= 49 = 5 : 2
   	38

   
   ∴  x = √49 = 7
   ∴  Number in the middle
   = 2x = 14

   Correct Option: B

   Let the numbers be 3x, 2x and 5x.
   According to the question,
   (3x)² + (2x)² + (5x)² = 1862
   ⇒  9x² + 4x² + 25x² = 1862
   ⇒  38x² = 1862
   

   ⇒  x2 =	1862	= 49 = 5 : 2
   	38

   
   ∴  x = √49 = 7
   ∴  Number in the middle
   = 2x = 14

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414. If 2r = h + √r² + h² then the ratio r : h (r ≠ 0) is

1. 1. 1 : 2

   
   
   

   2. 2 : 3

   
   
   

   3. 4 : 3

   
   
   

   4. 3 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   2r = h + √r² + h²
   ⇒  2r – h = √r² + h²
   On squaring both sides,
   4r² + h² – 4rh = r² + h²
   ⇒  3r² = 4rh
   ⇒  3r = 4h
   

   ⇒	r	=	4
   	h		3

   
   = 4 : 3

   Correct Option: C

   2r = h + √r² + h²
   ⇒  2r – h = √r² + h²
   On squaring both sides,
   4r² + h² – 4rh = r² + h²
   ⇒  3r² = 4rh
   ⇒  3r = 4h
   

   ⇒	r	=	4
   	h		3

   
   = 4 : 3

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415. A box of sweets was distributed between A and B in the ratio 3 : 4. If A got 36 sweets, what was the total number of sweets?

1. 1. 12

   
   
   

   2. 84

   
   
   

   3. 144

   
   
   

   4. 27

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of sweets be x.
   A : B = 3 : 4
   Sum of the terms of ratio
   = 3 + 4 = 7
   

   ∴   A’s share =	3x
   	7

   
   

   ∴	3x	= 36
   	7

   
   ⇒  3x = 36 × 7
   

   ⇒  x =	36 × 7	= 84
   	3

   Correct Option: B

   Let the number of sweets be x.
   A : B = 3 : 4
   Sum of the terms of ratio
   = 3 + 4 = 7
   

   ∴   A’s share =	3x
   	7

   
   

   ∴	3x	= 36
   	7

   
   ⇒  3x = 36 × 7
   

   ⇒  x =	36 × 7	= 84
   	3

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