In what ratio must water be mixed with milk to gain $16\frac{2}{3}\mathrm{\%}$ on selling the mixture at cost price?

Let x litres of water be mixed with y litres of milk, then

C.P. of (x + y) litres

= C.P. of $\left(y+16\frac{2}{3}\mathrm{\%}\text{ of }y\right)\text{ litres }$

i.e $x+y=\left(1+\frac{50}{300}\right)y=\frac{7}{6} y$

$\begin{array}{l}\Rightarrow 6x+6y=7y\Rightarrow 6x=y\\ \Rightarrow x:y=1:6\end{array}$

$\therefore$ Option (a) is the correct answer.