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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 :

If not more than two pegs of each cocktail is available, what can be the maximum percentage of White Rum in a drink obtained by mixing two or more cocktails at the Happily Tipsy Bar, if the cost per peg of the resulting drink should be at most Rs 280 ?

 

Option: 1

25%    


Option: 2

27.5% 


Option: 3

35%


Option: 4

37%


Answers (1)

best_answer

The first priority is to mix two cocktails to stay below the Rs 280 per peg cost cap. 

Teqnical is a perfect first choice considering the second highest content of White Rum and the lowest cost per peg. 

Also since we require maximum concentration of White Rum, and the highest is present in Hard Haddock, so even though Hard Haddock is the most expensive cocktail, it becomes the next choice. 

Selecting any other cocktail other than Hard Haddock would bring the concentration of White Rum down than what it is in Teqnical. 

That is also precisely the reason why we would not mix any third cocktail. 

Now, the ratio of mixing the two cocktails (Hard Haddock and Teqnical) cannot be anything else other than a) 2 : 1, or b) 1 : 2, or c) 2 : 2 = 1 : 1 respectively, as only two pegs of each cocktail is available. 

a) Ratio of 2 : 1 :

(x-32)/(42-x) = 2/1 

or, x – 32 = 84 – 2x

or, 3x = 116

or, x = 38.67% (where x is the final concentration of White Rum).

Cost per peg = (400*2 + 160*1)/3 = Rs 320 per peg, which is > Rs 280 per peg.

Hence it is not the desired ratio. 

b) Ratio of 1 : 2 :

(x-32)/(42-x) = 1/2 

or, 2x – 64 = 42 – x

or, 3x = 106

or, x = 35.33% (where x is the final concentration of White Rum).

Cost per peg = (400*1 + 160*2)/3 = Rs 240 per peg, which is < Rs 280 per peg.

Hence this may be the desired ratio.

c) Ratio of 2 : 2 = 1 : 1 :

x = (42+32)/2 = 37% (where x is the final concentration of White Rum).

Cost per peg = (400 + 160)/2 = Rs 280 per peg, which is permissible.

Hence this also may be the desired ratio.

However we get the highest concentration of White Rum as 37% fulfilling the criterion of price being ≤ Rs 280 per peg when the ratio of Hard Haddock and Teqnical is 1 : 1

Posted by

Anam Khan

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