Question : Two equal glasses filled with alcohol and water in the proportions 2 : 1 and 3 : 2 are emptied into a third glass. The proportion of alcohol and water in the third glass will be:
Option 1: 13 : 17
Option 2: 19 : 17
Option 3: 13 : 11
Option 4: 19 : 11
Correct Answer: 19 : 11
Solution :
Given: Ratio of alcohol and water in the first glass = 2 : 1
The ratio of alcohol and water in the second glass = 3 : 2
Let the quantity of mixture in each glass be 1 unit.
Alcohol in the first glass = $\frac{2}{3}$
Water in the first glass = $\frac{1}{3}$
Alcohol in the second glass = $\frac{3}{5}$
Water in the second glass = $\frac{2}{5}$
Ratio of their mixtures = $(\frac{2}{3}+\frac{3}{5}):(\frac{1}{3}+\frac{2}{5})=\frac{19}{15}:\frac{11}{15}= 19:11$
Hence, the correct answer is 19 : 11.
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