# CAT Practice : Averages, Ratios, Mixtures

When we mix two mixtures in a particular ratio, we get a third mixture. Given the third mixture how does one find the ratio in which they were mixed.

## Alligation

Q.28: A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?
1. 3.33 litres
2. 4 litres
3. 5.67 litres
4. 7.14 litres

Choice D. 7.14 litres

## Detailed Solution

Alcohol content in the alcohol to be added = 100%
Therefore, the allegation diagram for this problem can be drawn as:

Therefore, ratio of the mixture to alcohol = $\frac{70}{5} = \frac{14}{1}$
So, alcohol to be added = $\frac{100}{14}$

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