Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The content of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (ca

Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The content of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 litres) completely in order that the resulting may be half milk and half water? 

Given, two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively.

Amount of water in 1^st vessel = 1/9

Amount of water in 2^nd vessel = 5/6

Final mixture has half milk and half water

Amount of water in 3^rd vessel = ½

Let the volume taken from 1^st vessel be x, then the volume of mixture is taken from 2^nd vessel = 26 – x

$(\begin{array}{l} \therefore \;\frac{1}{9}\; \times \;x\; + \;\frac{5}{6}\left( {26 - x} \right)\; = \;\frac{1}{2}\; \times \;26\\ \Rightarrow \;\frac{{5\; \times \;26}}{6}\; + \;\frac{x}{9} - \frac{{5x}}{6}\; = \;\frac{{26}}{2}\\ \Rightarrow \;\frac{{13x}}{{18}}\; = \;\frac{{26}}{3} \end{array})$

⇒ x = 12 litres

Volume drawn from 2^nd vessel = 26 – 12 = 14 litres

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