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Averages Alligations & Mixtures Question

## Averages Alligations & Mixtures Question

Jewel Sheikh, asked 3 months ago

A vessel has 20L pure milk.
4L of pure milk is replaced with water. 4L of resulting mixtures is then replaced with water. Find the ratio of milk and water in the resulting mixture.
What is the quickest way to solve this question?

The best method to solve any Alligations and Mixtures problem is to go by the basics and apply unitary method. Formulae & shortcuts, no matter how convenient to use, work only under certain defined circumstances and fail in a nuanced setup. Hence going by the basics it what is generally recommended to students taking CAT. However, for the given problem statement, there does exist a formula:
Suppose a container contains x of liquid from which y units are taken out and replaced by water.

After n operations, the quantity of pure liquid = [x{1-(y/x)}^n]

You can use this formula to leapfrog into your calculations, but note very cautiously what ‘x’ &’y’ denote.
Hope that helps! :).

Ankit Doshi, IIM Indore (Since 1996)