Three vessels whose capacities are in the ratio of 3 : 2 : 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. Taking $$\frac{1}{3}$$ of first, $$\frac{1}{2}$$ of second and $$\frac{1}{7}$$ of third mixture, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is -

Solution(By Examveda Team)

Capacities of vessels
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3:2:1$$
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{M}}\,{\text{:}}\,{\text{W}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{T}}\,\,{\text{Mixture}} \cr & {\text{V - 1}} \to {{\text{(}}5\,\,\,:2\,\,\, = \,\,\,\,\,7{\text{)}}_{ \times 5}} \cr & {\text{V - 2}} \to {{\text{(4}}\,\,\,:1\,\,\, = \,\,\,\,\,5{\text{)}}_{ \times 7}} \cr & {\text{V - 3}} \to {{\text{(4}}\,\,\,:1\,\,\, = \,\,\,\,\,5{\text{)}}_{ \times 7}} \cr} $$
Equate the mixture
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{M}}\,{\text{:}}\,{\text{W}}\,\,\,\,\,\,\,\,\,\,{\text{T}}\,\,{\text{Mixture}} \cr & \left( {{\text{V - 1}}} \right) \to 25:10\,\,\,\,\,\,\, = 35 \cr & \left( {{\text{V - 2}}} \right) \to 28:7\,\,\,\,\,\,\,\, = 35 \cr & \left( {{\text{V - 3}}} \right) \to 28:7\,\,\,\,\,\,\,\, = 35 \cr} $$
$$\eqalign{ & {\text{Capacities}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{M}}:{\text{W}}\,\,\, = {\text{Total Mix}}{\text{.}} \cr & \left( {{\text{V}} - 1} \right) \times 3\, \to 75:30\,\,\, = 105 \cr & \left( {{\text{V}} - 2} \right) \times 2 \to 56:14\,\,\, = 70 \cr & \left( {{\text{V}} - 1} \right) \times 1\, \to 28:7\,\,\,\, = 35 \cr} $$
Water taken out
$$ \Rightarrow \frac{1}{3}{\text{ of water in (V - 1)}}$$     $$ + \frac{1}{2}{\text{ of water in (V - 2)}}$$     $$ + \frac{1}{7}{\text{ of water in (V - 3)}}$$
$$\eqalign{ & \Rightarrow \frac{1}{3} \times 30 + \frac{1}{2} \times 14 + \frac{1}{7} \times 7 \cr & \Rightarrow 10 + 7 + 1 \cr & \Rightarrow 18 \cr} $$
Similarly mixture will be
$$ \Rightarrow \frac{1}{3} \times 105 + \frac{1}{2} \times 70 + \frac{1}{7}$$     × 35
⇒ 75
$$\eqalign{ & \therefore \% {\text{ of water = }}\frac{{18}}{{75}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 24\% \cr} $$