166. A vessel full of pure acid contains 10 litres of it, of which 2 litres are withdrawn. The vessel is then filled with water. Next 2 litres of the mixture are withdrawn, and again the vessel is
     filled up with water. The ratio of the acid left in the vessel with that of the original quantity is

1. 1. 1 : 5

   
   
   

   2. 4 : 5

   
   
   

   3. 4 : 25

   
   
   

   4. 16 : 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Quantity of remaining acid = Initial quantitiy
   

   	1 −	Quantity taken out		n
   		Total initial quantity

   
   

   = 10		1 −	2		2	= 10 ×		4		2
   			10					5

   
   

   = 10 ×	4	×	4	=	32	litres
   	5		5		5

   
   

   Required ratio =	32	: 10
   	5

   
   = 32 : 50
   = 16 : 25

   Correct Option: D

   Quantity of remaining acid = Initial quantitiy
   

   	1 −	Quantity taken out		n
   		Total initial quantity

   
   

   = 10		1 −	2		2	= 10 ×		4		2
   			10					5

   
   

   = 10 ×	4	×	4	=	32	litres
   	5		5		5

   
   

   Required ratio =	32	: 10
   	5

   
   = 32 : 50
   = 16 : 25

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167. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water ?

1. 1. 1 : 1

   
   
   

   2. 1 : 2

   
   
   

   3. 2 : 3

   
   
   

   4. 3 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   G = 19W and C = 9W
   Let 1 gm of gold is mixed with x gm of copper such that (x + 1) gm of alloy is formed.
   ∴  19W + 9Wx = (x + 1) × 15W
   ⇒  19 + 9x = 15x + 15
   ⇒  15x – 9x = 19 – 15 ⇒ 6x = 4
   

   ⇒  x =	2
   	3

   
   

   ∴  Gold : Copper = 1 :	2
   	3

   
   = 3 : 2

   Correct Option: D

   G = 19W and C = 9W
   Let 1 gm of gold is mixed with x gm of copper such that (x + 1) gm of alloy is formed.
   ∴  19W + 9Wx = (x + 1) × 15W
   ⇒  19 + 9x = 15x + 15
   ⇒  15x – 9x = 19 – 15 ⇒ 6x = 4
   

   ⇒  x =	2
   	3

   
   

   ∴  Gold : Copper = 1 :	2
   	3

   
   = 3 : 2

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168. 80 litres of a mixture contains milk and water in the ratio of 27 : 5. How much more water is to be added to get a mixture containing milk and water in the ratio of 3 : 1 ?

1. 1. 5 litres

   
   
   

   2. 10 litres

   
   
   

   3. 15 litres

   
   
   

   4. 20 litres

   
   
   

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1. View Hint View Answer Discuss in Forum

   In 80 litres of mixture,
   Milk : Water = 27 : 5
   

   ∴  Milk ⇒	27	× 80 = 67.5 litres
   	32

   
   Water ⇒ 80 – 67.5 = 12.5 litres
   Let x litres of water is mixed.
   According to question,
   

   67.5	=	3
   12.5 + x		1

   
   ⇒  37.5 + 3x = 67.5
   ⇒  3x = 67.5 – 37.5 = 30
   ⇒  x = 10 litres

   Correct Option: B

   In 80 litres of mixture,
   Milk : Water = 27 : 5
   

   ∴  Milk ⇒	27	× 80 = 67.5 litres
   	32

   
   Water ⇒ 80 – 67.5 = 12.5 litres
   Let x litres of water is mixed.
   According to question,
   

   67.5	=	3
   12.5 + x		1

   
   ⇒  37.5 + 3x = 67.5
   ⇒  3x = 67.5 – 37.5 = 30
   ⇒  x = 10 litres

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169. The ratio of two liquids in a mixture is 3 : 5 and that in another mixture is 6 : 1. The ratio in which these two mixtures should be mixed so as to make the ratio of the liquids 7 : 3 is

1. 1. 44 : 71

   
   
   

   2. 44 : 81

   
   
   

   3. 44 : 91

   
   
   

   4. 44 : 61

   
   
   

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1. View Hint View Answer Discuss in Forum

   By the rule of alligation
   
   

   ∴  Required ratio =	11	:	13
   	70		4

   
   = 11 × 4 : 13 × 7
   = 44 : 91

   Correct Option: C

   By the rule of alligation
   
   

   ∴  Required ratio =	11	:	13
   	70		4

   
   = 11 × 4 : 13 × 7
   = 44 : 91

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170. A vessel contains 20 litres of acid. 4 litres of acid is taken out of the vessel and replaced by the same quantity of water. Next 4 litres of the mixture are withdrawn, and again the vessel is filled with the same quantity of acid left in the vessel with the quantity of acid initially in the vessel is

1. 1. 4 : 5

   
   
   

   2. 4 : 25

   
   
   

   3. 16 : 25

   
   
   

   4. 1 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Remaining acid = Initial quantity
   

   	1 −	quantity taken out
   		Original quantity

   
   

   = 20		1 −	4		2
   			20

   
   

   = 20		1 −	1		2
   			5

   
   

   = 20 ×	4	×	4
   	5		5

   
   = 12. 8 litres
   ∴  Required ratio = 12.8 : 20
   = 128 : 200 = 16 : 25

   Correct Option: C

   Remaining acid = Initial quantity
   

   	1 −	quantity taken out
   		Original quantity

   
   

   = 20		1 −	4		2
   			20

   
   

   = 20		1 −	1		2
   			5

   
   

   = 20 ×	4	×	4
   	5		5

   
   = 12. 8 litres
   ∴  Required ratio = 12.8 : 20
   = 128 : 200 = 16 : 25

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