161. In an alloy, zinc and copper are in the ratio 1 : 2. In the second alloy, the same elements are in the ratio 2 : 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloy is

1. 1. 3 : 10

   
   
   

   2. 3 : 7

   
   
   

   3. 10 : 3

   
   
   

   4. 7 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   In first alloy, zinc =	1
   	3

   
   

   In second alloy, zinc =	2
   	5

   
   

   In the new alloy, zinc =	5
   	13

   
   By the rule of Alligation,
   
   ∴  Required ratio
   

   =		2	−	5		:		5	−	1
   		5		13				13		3

   
   

   =	26 − 25	:	15 − 13
   	65		39

   
   

   =	1	:	2	=	1	:	2
   	65		39		5		3

   
   = 3 : 10

   Correct Option: A

   In first alloy, zinc =	1
   	3

   
   

   In second alloy, zinc =	2
   	5

   
   

   In the new alloy, zinc =	5
   	13

   
   By the rule of Alligation,
   
   ∴  Required ratio
   

   =		2	−	5		:		5	−	1
   		5		13				13		3

   
   

   =	26 − 25	:	15 − 13
   	65		39

   
   

   =	1	:	2	=	1	:	2
   	65		39		5		3

   
   = 3 : 10

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162. A liquid ‘P’ is 1	3	times as heavy as water is
     	7

     1	2	times as heavy as another liquid ‘Q’.
     	5

     The amount of liquid ‘P’ that must be added to 7 litres of the liquid ‘Q’ so that the mixture may weigh as much as an equal volume of water, will be

1. 1. 7 litres

   
   
   

   2. 5	1	litres
      	6

   
   
   

   3. 5 litres

   
   
   

   4. 4	2	litres
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let x litres of liquid P be mixed
   to 7 litres of liquid Q.
   According to the question,
   

   x ×	10	+	5	× 7 = x + 7
   	7		7

   
   

   ⇒	10x	+ 5 = x + 7
   	7

   
   ⇒  10x + 35 = 7x + 49
   ⇒  10x – 7x = 49 – 35
   ⇒  3x = 14
   

   ⇒  x =	14	= 4	2	litres
   	3		3

   Correct Option: D

   Let x litres of liquid P be mixed
   to 7 litres of liquid Q.
   According to the question,
   

   x ×	10	+	5	× 7 = x + 7
   	7		7

   
   

   ⇒	10x	+ 5 = x + 7
   	7

   
   ⇒  10x + 35 = 7x + 49
   ⇒  10x – 7x = 49 – 35
   ⇒  3x = 14
   

   ⇒  x =	14	= 4	2	litres
   	3		3

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163. Acid and water are mixed in a vessel A in the ratio of 5 : 2 and in the vessel B in the ratio 8 : 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which the acid and water will be in the ratio of 9 : 4?

1. 1. 7: 2

   
   
   

   2. 2: 7

   
   
   

   3. 7: 4

   
   
   

   4. 2: 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   By alligation rule,
   
   

   =	65 − 63	=	2
   	91		91

   
   

   ∴  Required ratio =	2	:	1
   	91		13

   
   = 2 : 7

   Correct Option: B

   By alligation rule,
   
   

   =	65 − 63	=	2
   	91		91

   
   

   ∴  Required ratio =	2	:	1
   	91		13

   
   = 2 : 7

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164. There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1, in the second container 5 : 2. If they are mixed up, the ratio of milk to water in the mixture will be

1. 1. 28 : 41

   
   
   

   2. 41 : 28

   
   
   

   3. 15 : 41

   
   
   

   4. 41 : 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   Capacity of each container = x litre (let)
   In first container,
   

   Milk =	3x	litres,
   	4

   
   

   Water =	x	litres
   	4

   
   In second container,
   

   Milk =	5x	litres,
   	7

   
   

   Water =	2x	litres
   	7

   
   On mixing both,
   

   Quantity of milk =	3x	+	5x
   	4		7

   
   

   =	21x + 20x	=	41x	litres
   	28		28

   
   

   Quantity of water =	x	+	2x
   	4		7

   
   

   =	7x + 8x	litres =	15x	litres
   	28		28

   
   

   ∴  Required ratio =	41x	:	15x
   	28		28

   
   = 41 : 15

   Correct Option: D

   Capacity of each container = x litre (let)
   In first container,
   

   Milk =	3x	litres,
   	4

   
   

   Water =	x	litres
   	4

   
   In second container,
   

   Milk =	5x	litres,
   	7

   
   

   Water =	2x	litres
   	7

   
   On mixing both,
   

   Quantity of milk =	3x	+	5x
   	4		7

   
   

   =	21x + 20x	=	41x	litres
   	28		28

   
   

   Quantity of water =	x	+	2x
   	4		7

   
   

   =	7x + 8x	litres =	15x	litres
   	28		28

   
   

   ∴  Required ratio =	41x	:	15x
   	28		28

   
   = 41 : 15

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165. Two equal glasses filled with alcohol and water in the proportions 2 : 1 and 3 : 2 are emptied into a third glass. The proportion of alcohol and water in the third glass will be

1. 1. 13 : 17

   
   
   

   2. 19 : 17

   
   
   

   3. 13 : 11

   
   
   

   4. 19 : 11

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the volume of each glass be = x litres.
   ∴  Required ratio
   = Alcohal : water
   

   =		2x	+	3x		:		x	+	2x
   		3		5				3		5

   
   

   =		10x + 9x		:		5x + 6x
   		15				15

   
   = 19 : 11

   Correct Option: D

   Let the volume of each glass be = x litres.
   ∴  Required ratio
   = Alcohal : water
   

   =		2x	+	3x		:		x	+	2x
   		3		5				3		5

   
   

   =		10x + 9x		:		5x + 6x
   		15				15

   
   = 19 : 11

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