Multiple choice

How much skimmed milk (in kg) containing 0.1% fat should be added to 500 kg of cream containing 50% fat to produce standardised cream containing 36% fat?

  1. 140

  2. 165

  3. 195

  4. 210
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alligation method: Cream (50%) and Skimmed milk (0.1%) mixed to get 36%. Differences: |50 - 36| = 14 and |36 - 0.1| = 35.9. Ratio of cream to milk = 35.9 : 14. If 35.9 units = 500 kg, 1 unit = 13.927. Milk = 14 * 13.927 = 194.98, which rounds to 195 kg.

AI explanation

Using the method of alligation on the fat percentages, cream has 50% fat and skimmed milk has 0.1% fat. The desired standardized cream has a mean of 36% fat. The ratio of cream to skimmed milk is (36 minus 0.1) to (50 minus 36), which gives a ratio of 35.9 to 14. Setting up the proportion 500 divided by Skimmed Milk equals 35.9 divided by 14 yields Skimmed Milk equals 7000 divided by 35.9. This calculation shows approximately 195 kilograms of skimmed milk are required, rounding to the nearest integer.

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