# 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.30: A milkman purchases milk at Rs 20/litre and mixes 4 litres of water in it. By selling the resultant mixture at the rate of Rs 20/litre, he earns a profit of 40%. The amount of mixture he had with him to sell was:
1. 10 l
2. 12 l
3. 14 l
4. 4 l

Choice C. 14 l

## Detailed Solution

To earn a profit of 40% at Rs 20/litre,
Cost price = $\frac{20}{1.4} = \frac{100}{7}$

Therefore,
Milk: Water = $\frac{100}{7} : \frac{40}{7}$ = 5:2
So, in 4 litres of water, 10 litres of milk would be required. Resultant mixture = 14 litres

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