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  • Directions for question : At the Happily Tipsy Bar, the chief bar-tender, after a lot of experimentation found out t

Directions for question :

At the Happily Tipsy Bar, the chief bar-tender, after a lot of experimentation found out that Vodka, White Rum, Gin and Tequila if mixed in different concentrations can create four very exciting cocktails which he named as the Teqnical, the Hard Haddock, the Fiery Ginie and the Russian Heat. The respective percentage alcohol concentrations of the cocktails are provided in the chart below. 

He priced them at Rs 160, Rs 400, Rs 320 and Rs 240 per single peg respectively. On specific orders from customers, he was ready to mix two or more drinks in the ratio as fancied by the customer.

Alcohol Vodka White Rum Gin Tequila
Cocktail
TEQNICAL 18 32 8 42
HARD HADDOCK 8 42 32 18
FIERY GINIE 9 27 37 27
RUSSIAN HEAT 42 13 37 8

Question :

A customer at the Happily Tipsy Bar asks for a peg of a drink with a single portion each of Teqnical, Fiery Ginie and Russian Heat, and a double portion of Hard Haddock. What will be the minimum integral ratio of the percentage contents of Vodka, White Rum, Gin and Tequila in that drink ? 

Option: 1

112 : 121 : 105 : 110


Option: 2

85 : 156 : 146 : 113


Option: 3

35 : 32 : 41 : 31    


Option: 4

105 : 121 : 98 : 108


Answers (1)

best_answer

On mixing one unit each of Teqnical, Fiery Ginie and Russian Heat, the resultant percentage quantities are as follows :

Vodka : (18+9+42)/3 = 69/3 = 23%,

White Rum : (32+27+13)/3 = 72/3 = 24%,

Gin : (8+37+37)/3 = 82/3 = 27.33%, and

Tequila : (42+27+8)/3 = 77/3 = 25.67%

On mixing two units of Hard Haddock with three units of the mixture, the resultant percentage quantities are :

Vodka :

(x-8)/(23-x) = 3/2

or, 2x – 16 = 69 – 3x

or, 5x = 85

or, x = 17%,

White Rum :

(x-24)/(42-x) = 2/3

or, 3x – 72 = 84 – 2x

or, 5x = 156

or, x = 31.2%,

Gin :

(x-27.33)/(32-x) = 2/3

or, 3x – 82 = 64 – 2x

or, 5x = 146

or, x = 29.2%, and

Tequila :

(x-18)/(25.67-x) = 3/2

or, 2x – 36 = 77 – 3x

or, 5x = 113

or, x = 22.6%

Hence, the minimum integral ratio of the percentage contents of Vodka, White Rum, Gin and Tequila in that drink ordered by the customer at Happily Tipsy Bar is

= 17 : 31.2 : 29.2 : 22.6

= 85 : 156 : 146 : 113

Posted by

Pankaj

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