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I can't seem to to find a way to solve this problem:

In a mixture $60$ litres, the ratio of alcohol and water is $2:1$. If this ratio is to be $1:2$ then the quantity of water further added is? Ans $60$ litres

Any suggestions?

2 Answers 2

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In the original 60 liter mixture, the ratio of alcohol to water was $2:1$ which means that the original mixture was two-thirds alcohol and one-third water. This means $\frac{2}{3}\cdot 60 = 40$ liters of alcohol and $\frac{1}{3}\cdot 60 = 20$ liters of water.

Now you want to change the ratio to $1:2$ by adding water. a $1:2$ ratio means one-third alcohol and two-thirds water. Since we are adding only water, the amount of alcohol in the final mixture is still going to be $40$ liters (same as in your original mixture).

Now we know that $40$ liters of alcohol is one-third of the new mixture, which means there has to be $\dfrac{2/3}{1/3} \cdot 40 = 2\cdot 40 = 80$ liters of water in the new mixture. Since we already had $20$ liters originally, we have to add $80-20 = 60$ liters.

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    Yes it does. Thanks.2012-07-03
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Hint: in the original mixture, how much is alcohol? How much is water? Given the amount of alcohol, which doesn't change, how much water is needed to make the solution 1:2?