291. Find the mean proportional between 100 and 625.

1. 1. 350

   
   
   

   2. 225

   
   
   

   3. 250

   
   
   

   4. 275

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the mean proportional be x.
   ∴  100 : x : x : 625
   

   Then ,	100	=	x
   	x		625

   
   ⇒  x² = 100 × 625
   ⇒  x = √100 × 625 = 10 × 25
   = 250

   Correct Option: C

   Let the mean proportional be x.
   ∴  100 : x : x : 625
   

   Then ,	100	=	x
   	x		625

   
   ⇒  x² = 100 × 625
   ⇒  x = √100 × 625 = 10 × 25
   = 250

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292. Determine the fourth proportional to 9 .6 m 7 .2 m 28.8 m .

1. 1. 22.6 m .

   
   
   

   2. 21.6 m .

   
   
   

   3. 23.6 m .

   
   
   

   4. 20.6 m .

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the fourth proportional be x.
   ∴  9.6 kg : 7.2 kg . : : 28.8 m : xm
   o r, 9.6 : 7.2 : : 28.8 : x
   

   Then ,	9.6	=	28.8
   	7.2		x

   
   ⇒  9.6 × x = 7.2 × 28.8
   

   ⇒  x =	7.2 × 28.8	= 21.6 m
   	9.6

   Correct Option: B

   Let the fourth proportional be x.
   ∴  9.6 kg : 7.2 kg . : : 28.8 m : xm
   o r, 9.6 : 7.2 : : 28.8 : x
   

   Then ,	9.6	=	28.8
   	7.2		x

   
   ⇒  9.6 × x = 7.2 × 28.8
   

   ⇒  x =	7.2 × 28.8	= 21.6 m
   	9.6

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293. If x : y = 8 : 9 , then 5 x – 4 y : 3 x + 2 y is equal to :

1. 1. 2 : 19

   
   
   

   2. 3 : 17

   
   
   

   3. 2 : 21

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   x	;	8	(Given)
   y		9

   
   

   ∴   (5x + 4y / 3x) 2y) ;	5	x			+ 4
   		y
   	3	x	) 2
   		y

   
   

   ;	5 "	8			+ 4
   			9
   	3 "	8	) 2
   		9

   
   

   ;	40 + 36	;	4	;	2
   	24) 18		42		21

   Correct Option: C

   x	;	8	(Given)
   y		9

   
   

   ∴   (5x + 4y / 3x) 2y) ;	5	x			+ 4
   		y
   	3	x	) 2
   		y

   
   

   ;	5 "	8			+ 4
   			9
   	3 "	8	) 2
   		9

   
   

   ;	40 + 36	;	4	;	2
   	24) 18		42		21

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294. A mixture contains alcohol and water in the ratio 4 : 3 . If 5 litres of water is added to the mixture the ratio becomes 4 : 5 . The quantity of alcohol in the given mixture is :

1. 1. 12 litres

   
   
   

   2. 10 litres

   
   
   

   3. 14 litres

   
   
   

   4. 16 litres

   
   
   

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1. View Hint View Answer Discuss in Forum

   4x	;	4
   3x) 5		5

   
   ⇒  20x = 12x + 20
   ⇒  8x = 20 ⇒ x = 2.5
   ∴  Quantity of alcohol
   = 4 × 2.5 = 10 litres

   Correct Option: B

   4x	;	4
   3x) 5		5

   
   ⇒  20x = 12x + 20
   ⇒  8x = 20 ⇒ x = 2.5
   ∴  Quantity of alcohol
   = 4 × 2.5 = 10 litres

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295. Twenty years ago the ratio between the ages of Sita and Meena was 1 : 4 and at present it is 1 : 2 . What is the age of Sita at present?

1. 1. 25

   
   
   

   2. 35

   
   
   

   3. 30

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   20 years ago,
   Sita’s age = x years
   Meena’s age = 4x years
   

   ∴	x) 20	;	1
   	4x) 20		2

   
   ⇒  2x + 40 = 4x + 20
   ⇒  2x = 20 ⇒ x = 10
   ∴  Sita’s present age = 30 years

   Correct Option: C

   20 years ago,
   Sita’s age = x years
   Meena’s age = 4x years
   

   ∴	x) 20	;	1
   	4x) 20		2

   
   ⇒  2x + 40 = 4x + 20
   ⇒  2x = 20 ⇒ x = 10
   ∴  Sita’s present age = 30 years

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