Question

Skim milk is prepared by the removal of some of the fat from whole milk. This skim milk is found to contain 90.5% water, 3.5% protein, 5.1% carbohydrate, 0.1% fat and 0.8% ash. If the original milk contained 4.5% fat, Calculate its composition assuming that fat only was removed to make the skim milk and that there are no losses in processing.

(a) Fat = 4.5%, Water = 86.5%, protein = 3.3%, carbohydrate = 4.9%, ash = 0.8%

(b) Fat = 4.5%, Water = 83.5%, protein = 3.0%, carbohydrate = 4.5%, ash = 0.9%

(c) Fat = 4.6%, Water = 80.5%, protein = 3.5%, carbohydrate = 4.0%, ash = 0.9%

(d) Fat = 4.6%, Water = 81.5%, protein = 3.3%, carbohydrate = 4.5%, ash = 0.8%

This question was addressed to me during an interview.

My enquiry is from Energy Balance Numericals Without Reactions topic in chapter Energy Balance of Bioprocess Engineering

Answer 1

Right choice is (a) Fat = 4.5%, Water = 86.5%, protein = 3.3%, carbohydrate = 4.9%, ash = 0.8%

Easy explanation: Basis: 100 kg of skim milk.

This contains, therefore, 0.1kg of fat. Let the fat which was removed from it to make skim milk be x kg.

Total original fat = (x + 0.1) kg

Total original mass = (100 + x) kg

and as it is shown that the original fat content was 4.5% so,

(x+0.1)/(100+x) = 0.045

where = x+0.1 = 0.045(100+x)

x = 4.6 kg

So the composition of the whole milk is then fat = 4.5%, water = 90.5/104.6 = 86.5%, protein = 3.5/104.6 = 3.3%, carbohydrate = 5.1/104.6 = 4.9% and ash = 0.8%.