# 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.37: What would be the ratio of milk and water in a final mixture formed by mixing milk and water that are present in three vessels of capacity 1l, 2l, and 3l respectively and in the ratios 5:1, 3:2 and 4:3 respectively?
1. 747:443
2. 787:1260
3. 787:473
4. 747:473

Choice C. 787:473

## Detailed Solution

Solve this type of questions by taking 2 at a time. Take the first 2 vessels,
In 1st, fraction of milk = $\frac{5}{6}$
In 2nd, fraction of milk = $\frac{3}{5}$
Therefore,

= ) $\frac{\frac{3}{5} - x}{x - \frac{5}{6}} = \frac{1}{2}$
= ) $\frac{6}{5} - 2x = x - \frac{5}{6}$
= ) $\frac{6}{5} + \frac{5}{6} = 3x$
= )$x = \frac{61}{90}$ (And the volume of mixture after mixing = 1 + 2 = 3 l)
Therefore,

= ) $\frac{\frac{4}{7} - x}{x - \frac{61}{90}} = \frac{3}{3}$
= ) $\frac{4}{7} - x = x + \frac{61}{90}$
= ) $\frac{4}{7} + \frac{61}{90} = 2x$
= ) $2x = \frac{787}{630} => x = \frac{787}{1260}$
Therefore, Milk : Water = $\frac{787}{(1260 - 787)} = \frac{787}{473}$

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