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A vessel has a milk solution in which milk and water are in the ratio $4:1$. By addition of water to it, milk solution with milk and water in the ratio $4:3$ was formed. On replacing $14\;\text{L}$ of this solution with pure milk the ratio of milk and water changed to $5:3$. What is the volume of the water added?

  1. $12\;\text{L}$
  2. $60\;\text{L}$
  3. $32\;\text{L}$
  4. $24\;\text{L}$
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Initial ratio of milt to water $ = 4:1$

So, if $4x$ amount of milk is there, $x$ amount of water is there.

Let $y$ be the amount of water added. Now, the ratio changes to $4:3.$ i.e., for $4x$ amount of milk, now there is $3x$ amount of water. So, we get that $y = 2x.$

In $14l,$ amount of water $= \frac{3}{3+4} \times14 = 6l$

Given, $\frac{4x+6}{3x-6} = \frac{5}{3}$

$\implies 12x + 18 = 15x -30$

$\implies x = 16$

$y = 2x = 32.$

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