To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

1^st Method (Method of Alligation):
Let the quantity of water to be mixed is x kg.
Let cost of milk be Rs. 1 per kg.
Then SP of 50 kg of milk with gain 10% = Rs. 55 [As Cost of 50 kg milk = Rs. 50, then SP = (50 + 10% of 50)]

Then, water to be mixed is 5 kg, As the selling price of the milk is Rs. 1 per kg. Seller has to have 10% gain on 50 kg milk, he must have to add 5 kg water to 50 kg milk.

2^nd Method (Simple Method):
Let the quantity of water mixed be x kg.
Let CP of 1 kg of pure milk = Rs. 1.
Hence,
% gain = x × $$\frac{{100}}{{50}}$$
10 = $$\frac{{100{\text{x}}}}{{50}}$$
Or, 2x = 10
or, x = 5 kg.