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A vessel contains milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From this resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk water in the final solution is 3 : 7. Find the original volume of the solution.

A vessel contains milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From this resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk water in the final solution is 3 : 7. Find the original volume of the solution. Correct Answer 80 L

Let the original volume be x. then, quantity of milk and water, = $$\frac{{3x}}{5}$$ and $$\frac{{2x}}{5}$$ respectively. After adding water to it, the volume becomes 150%, the quantity of milk and water, = $$\frac{{3x}}{5}$$ and $$\frac{{9x}}{10}$$$$\frac{{\frac{{3x}}{5} - 12}}{{\frac{{9x}}{{10}} + 12}} = \frac{3}{7}$$14(3x - 60) = 3(9x + 120)Or, x = 80 L

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