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 ?
112 : 121 : 105 : 110
85 : 156 : 146 : 113
35 : 32 : 41 : 31
105 : 121 : 98 : 108
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