Question

Given 1200 kg of cream testing 55% fat. How much butter with 85% fat will be produced from it?

• A. 750 kg
• B. 776.5 kg
• C. 700 kg
• D. 685 kg

Hint:

Always remember: Fat is the conserved quantity. In actual plant practice, you would subtract a small percentage (about 0.5-1.0%) for fat lost in buttermilk.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In dairy arithmetic, we use the principle of mass balance. The total fat in the raw material (cream) must equal the total fat in the final product (butter), assuming no losses for this calculation.
Key Formula or Approach:
\[ \text{Total Fat in Cream} = \text{Total Fat in Butter} \] \[ \text{Mass of Cream} \times \frac{\% \text{Fat in Cream}}{100} = \text{Mass of Butter} \times \frac{\% \text{Fat in Butter}}{100} \]

Step 2: Detailed Explanation:
Given: - Mass of Cream ($M_{c}$) = 1200 kg - % Fat in Cream ($F_{c}$) = 55% - % Fat in Butter ($F_{b}$) = 85% - Mass of Butter ($M_{b}$) = ? 1. Calculate the total weight of fat in the cream: \[ \text{Fat weight} = 1200 \times 0.55 = 660 \text{ kg} \] 2. Set this fat weight equal to the fat in the butter: \[ 660 = M_{b} \times 0.85 \] 3. Solve for $M_{b}$: \[ M_{b} = \frac{660}{0.85} \approx 776.47 \text{ kg} \] Rounding to the nearest decimal provided in the options, we get 776.5 kg.

Step 3: Final Answer:
The amount of butter produced will be 776.5 kg.