# 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.26: 3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?
1. $\frac{2187}{100}$
2. $\frac{81}{19}$
3. $\frac{729}{271}$
4. $\frac{743}{229}$

Choice C. $\frac{729}{271}$

## Detailed Solution

Formulae (derived using allegation):
Milk left = Capacity x (1 – fraction of milk withdrawn)n
Therefore, milk left = 30 x 0.93
= ) $30 * \frac{9}{10} * \frac{9}{10} * \frac{9}{10}$
= ) $\frac{2187}{100}$
So, Water in container = 30 – $\frac{2187}{100}$
= ) $\frac{(3000 - 2187)}{100}$
=) $\frac{813}{100}$
Therefore, Milk : Water = 2187 : 813 = 729 : 271

Correct Answer: $\frac{729}{271}$

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