If water was mixed with milk by milkman to gain $\frac{50}{3}$ % on selling the mixture at cost price, then percentage of water in the mixture :

$14\frac{2}{7}$

The correct answer is Option (4) → $14\frac{2}{7}$

Assume the cost of milk be = 1

Cost of mixture per liter = Cost of milk × $\left(\frac{1-gain\,percentage}{100}\right)$

$=1×\left(1-\frac{\frac{50}{3}}{100}\right)$

$=1×\left(1-\frac{1}{6}\right)$

$=\frac{5}{6}$

Ratio of water to milk = $\frac{Cost\,of\,milk-Cost\,of\,mixture}{Cost\,of\,mixture}$

$=\frac{1-\frac{5}{6}}{\frac{5}{6}}$

$=\frac{1}{5}$

∴ Mixture has 1 part of water and 5 parts of milk

Now,

Percentage of water = $\frac{Parts\, of\, water}{Total\,water}×100$

$=\frac{1}{1+5}×100$

$=\frac{1}{6}×100$

$=16.67%$