A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :

Profit (%) = 9.09 % = 1/11

Since the ratio of water and milk is  1 : 11,

Therefore the ratio of water is to mixture = 1:12

Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml