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A vessel contains a mixture of water and alcohol in the ratio 2:1. Twelve litres of the mixture is removed and replaced with water, and the final ratio becomes 4:1. What is the amount of alcohol in the initial mixture?

1. 12 litres
2. 15 litres
3. 20 litres
4. 10 litres

Correct answer: 10 litres

Solution

Let the initial mixture be 3 parts, with alcohol = 1 part and water = 2 parts. If total volume is $x$, then initial alcohol = $x/3$. After removing 12 litres, alcohol removed = 4 litres and water removed = 8 litres. Replacing with 12 litres of water changes the ratio to 4:1, which gives the initial alcohol as 10 litres.

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