Given that, let the capacity of three vessels are 3x, 2x and x liter.

Now, taking three vessels separately

Vessel - 1: Mixture taken out = $3x\times \frac{1}{3}$ = x liter

$\therefore$Amount of milk=$\frac{5x}{7}$and amount of water = $\frac{2x}{7}$

Vessel - 2; Mixture taken out = $2x\times \frac{1}{2}$ = x liter

$\therefore$Amount of milk$=\frac{4x}{5}$ and amount of water =$\frac{x}{5}$

Vessel - 3: Mixture taken out = $x\times \frac{1}{7}=\frac{x}{7} Liter$

$\therefore$Amount of milk $\frac{4x}{35}$= and amount of water =$\frac{x}{35}$

Total milk $=\frac{5x}{7}+\frac{4x}{5}+\frac{4x}{35}=\frac{25x+28x+4x}{35}=\frac{57x}{35}$

$\therefore$Total volume of mixture=x+x+ $\frac{x}{7}=\frac{7x+7x+x}{7}=\frac{15x}{7}$

$\therefore$Percentage of milk =$\frac{100\times {\displaystyle \frac{57x}{35}}}{{\displaystyle \frac{15x}{7}}}=\frac{100\times 57x}{35}\times \frac{7}{15x}=\frac{39900}{525}=76\%$

$\therefore$Percentage of water = (100 - 76)% = 24%