591. In what ratio must a grocer mix tea at $ 60 a kg, and $ 65 a kg, so that by selling the mixture at $ 68.20 a kg, he may gain 10%?

1. 1. 3 : 2

   
   
   

   2. 3 : 4

   
   
   

   3. 3 : 5

   
   
   

   4. 4 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given in question , S.P. of 1 kg mixture = $ 68.20, Gain = 10%
   

   ∴ C.P. of 1 kg mixture = $		68.20 ×	100			= $ 62
   			110

   
   By the rule of alligation,
   
   

   Correct Option: A

   Given in question , S.P. of 1 kg mixture = $ 68.20, Gain = 10%
   

   ∴ C.P. of 1 kg mixture = $		68.20 ×	100			= $ 62
   			110

   
   By the rule of alligation,
   
   ∴ Required ratio = 3 : 2
   

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592. The ratio in which the Darjeeling tea at $ 32 per kg is mixed with the Assam tea at $ 25 per kg so as to gain 20% by selling the mixture at $ 32.40 per kg is

1. 1. 4 : 3

   
   
   

   2. 3 : 4

   
   
   

   3. 5 : 2

   
   
   

   4. 2 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the C.P. of the mixture be $ p per kg, then
   

   p ×	120	= 32.40
   	100

   
   

   ⇒ p ×	32.40 × 100	= 27
   	120

   
   Using alligation method ,
   
   

   Correct Option: D

   If the C.P. of the mixture be $ p per kg, then
   

   p ×	120	= 32.40
   	100

   
   

   ⇒ p ×	32.40 × 100	= 27
   	120

   
   Using alligation method ,
   
   ∴ Required ratio = Price of Darjeeling tea : Price of Assam tea = 2 : 5

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593. The ratio of the quantities of sugar, in which sugar costing $ 20 per kg. and $ 15 per kg. should be mixed so that there will be neither loss nor gain on selling the mixed sugar at the rate of $ 16 per kg, is

1. 1. 2 : 1

   
   
   

   2. 1 : 2

   
   
   

   3. 4 :1

   
   
   

   4. 1 : 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let p kg of sugar costing 20/kg and q kg of sugar costing 15/kg are mixed.
   According to the question,
   20p + 15q = 16 (p + q)
   ⇒ 20p + 15q = 16p + 16q
   ⇒ 20p – 16p = 16q – 15q
   ⇒ 4p = q
   

   ∴		p	=	1	or 1 : 4
   		q		4

   
   We can find required answer with the help of given formula :
   By the rule of alligation ,
   

   Correct Option: D

   Let p kg of sugar costing 20/kg and q kg of sugar costing 15/kg are mixed.
   According to the question,
   20p + 15q = 16 (p + q)
   ⇒ 20p + 15q = 16p + 16q
   ⇒ 20p – 16p = 16q – 15q
   ⇒ 4p = q
   

   ∴		p	=	1	or 1 : 4
   		q		4

   
   We can find required answer with the help of given formula :
   By the rule of alligation ,
   
   ∴ Required ratio = 1 : 4

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594. In what ratio Darjeeling Tea costing $ 320 per kg be mixed with Assam Tea costing $ 250 per kg so that there is a gain of 20% by selling the mixture at $ 324 per kg?

1. 1. 1 : 2

   
   
   

   2. 2 : 3

   
   
   

   3. 3 : 2

   
   
   

   4. 2 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using alligation method ,
   

   CP of the mixture =	324 × 100	= $ 270
   	120

   
   
   

   Correct Option: D

   Using alligation method ,
   

   CP of the mixture =	324 × 100	= $ 270
   	120

   
   
   ∴ Required ratio = Cost of Darjeeling Tea : Cost of Assam Tea
   ∴ Required ratio = 20 : 50 = 2 : 5

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595. The ratio, in which tea costing $ 192 per kg is to be mixed with tea costing $ 150 per kg so that the mixed tea, when sold for $ 194.40 per kg, gives a profit of 20%, is

1. 1. 2 : 5

   
   
   

   2. 3 : 5

   
   
   

   3. 5 : 3

   
   
   

   4. 5 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   By the rule of allegation,
   

   CP of mixed tea =	100	× 194.40 = $ 162 / kg
   	120

   
   
   

   Correct Option: A

   By the rule of allegation,
   

   CP of mixed tea =	100	× 194.40 = $ 162 / kg
   	120

   
   
   

   ∴ Required ratio =		12	=	2	or 2 : 5
   		30		5

   
   

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