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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 From this resultant solution 30 L is withdrawn and then replaced with water.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. 80 L B. 65 L C. 75 L D. 82 L Answer: Option A
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Solution(By Apex Team)

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

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