Question

By using a Pearson Square method, calculate the amounts of orange juice (10 % sugar content) and sugar syrup (60 % sugar content) needed to produce 50 kg of fruit squash containing 15 % sugar.

• A. 5 Kg of orange juice & 45 Kg of Sugar Syrup
• B. 45 Kg of orange juice & 5 Kg of Sugar Syrup
• C. 40 Kg of orange juice & 10 Kg of Sugar Syrup
• D. 10 Kg of orange juice & 40 Kg of Sugar Syrup

Hint:

In the Pearson Square, the "difference" on the diagonal always tells you the "parts" of the ingredient at the *other* end of that line.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The Pearson Square method is a simplified tool for blending two ingredients to reach a specific target concentration. We need to find the proportion of 10% juice and 60% syrup to get a 15% final product.
Key Formula or Approach: 1. Place the target value (15) in the center of the square. 2. Place the ingredient concentrations (10 and 60) on the left corners. 3. Subtract diagonally (absolute values) to get parts on the right corners.

Step 2: Detailed Explanation:

• Diagonals:
• $|60 - 15| = 45$ parts (this is the proportion for the ingredient opposite - the 10% juice).
• $|10 - 15| = 5$ parts (this is the proportion for the 60% syrup).
• Total Parts: $45 + 5 = 50$ parts.
• Proportional calculation for 50 kg batch:
• Amount of 10% juice = $(\frac{45}{50}) \times 50 \text{ kg} = 45 \text{ kg}$.
• Amount of 60% syrup = $(\frac{5}{50}) \times 50 \text{ kg} = 5 \text{ kg}$.
• Verification: Total weight is $45 + 5 = 50$ kg. Total sugar is $(45 \times 0.10) + (5 \times 0.60) = 4.5 + 3.0 = 7.5$ kg. Final concentration is $\frac{7.5}{50} = 15\%$. It is correct.

Step 3: Final Answer: We need 45 kg of juice and 5 kg of sugar syrup.