# 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.33: A man buys juice at Rs 10/litre and dilutes it with water. He sells the mixtures at the cost price and thus gains 11.11%. Find the quantity of water mixed by him in every litre of juice.
1. 0.1 l
2. 0.909 l
3. 0.125 l
4. 0.111 l

Choice D. 0.111 l

## Detailed Solution

As we know 11.11% = $\frac{1}{9}$
Therefore, to gain 11.11%, C.P. + $\frac{1}{9}$ * C.P. = 10
= ) $\frac{10C.P}{9}$ = 10 = ) C.P. = Rs 9
Therefore,

So, Juice: Water = 9 : 1 With 1 litre of juice, water = $\frac{1}{9}$ * litre = 0.111 l
Note: Read the question carefully, it is saying per litre of juice and NOT per litre of mixture

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