# 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.34: Two tanks of similar volume are full of a mixture of oil and water. In the first, the ratio of oil and water is 5:8 and in the second, it is 7:19. If both these tanks are poured in a larger tank, what would be the resultant ratio of oil and water?
1. 1:3
2. 17:52
3. 151:304
4. 17:35

Choice D. 17:35

## Detailed Solution

In this type of questions, take one of the components and find its proportion in the overall mixture.
In first tank, Oil/Water = 5/8 therefore, Oil/Mixture = 5/13
In second tank, Oil/Water = 7/19 therefore, Oil/Mixture = 7/26
Therefore,

= ) $\frac{7}{26} – x = x – \frac{5}{13}$
= ) $\frac{7}{26} + \frac{5}{13}$ = 2x
= ) 2x = $\frac{(7+10)}{26}$
= ) x = $\frac{17}{52}$
Therefore, Oil : Mixture = $\frac{17}{52}$ = ) Oil : Water $= \frac{17}{(52-17)} = \frac{17}{35}$

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