Question : The ratio of spirit and water in two mixtures of 46 litres and 50 litres is 11 : 12 and 2 : 3 respectively. Both the mixtures are mixed. Find the ratio of the spirit and water in the new mixture.
Option 1: 8 : 9
Option 2: 7 : 9
Option 3: 5 : 6
Option 4: 3 : 7
Correct Answer: 7 : 9
Solution :
Given: The ratio of spirit and water in two mixtures of 46 litres and 50 litres is 11 : 12 and 2 : 3 respectively.
Both the mixtures are mixed.
In 46 litres of the mixture,
The amount of spirit = $\frac{11}{23}\times 46=22$ litres
The amount of water = 46 – 22 = 24 litres
In 50 litres of the mixture,
The amount of spirit = $\frac{2}{5}\times 50=20$ litres
The amount of water = 50 – 20 = 30 litres
The ratio of the spirit and water in the new mixture = (22 + 20) : (24 + 30) = 42 : 54 = 7 : 9
Hence, the correct answer is 7: 9.
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