Question

choose the correct answer.
42%
12%
8%
42%
12%
8%
part feed a
30 parts
the next step is to subtract diagonally.
what is the amount of part feed a?
54 parts
30 parts
20 parts
4 parts

Explanation:

Step1: Identify diagonal values

For Part Feed A, use the diagonal values: $42\%$ and $8\%$; the other diagonal is $12\%$ and $42\%$. The given reference amount is 30 parts.

Step2: Calculate difference for numerator

Subtract diagonally for the numerator: $42 - 8 = 34$? No, correct diagonal subtraction for alligation: The desired concentration is 12%, the two feeds are 42% and 8%. For the 42% feed (Part Feed A), the difference is $|12 - 8| = 4$. For the 8% feed, the difference is $|42 - 12| = 30$.

Step3: Set up ratio

The ratio of Part Feed A to the other feed is $4:30$. Wait, no: The total parts corresponding to the difference of the other component is 30 parts. So $\frac{\text{Part Feed A}}{30} = \frac{|12 - 8|}{|42 - 12|}$

Step4: Solve for Part Feed A

$\text{Part Feed A} = 30 \times \frac{4}{30} = 4$ parts? No, wait, correct alligation: Let $x$ be Part Feed A (42%). The mixture is 12%, the other feed is 8% with 30 parts.
Mass balance: $0.42x + 0.08 \times 30 = 0.12(x + 30)$
$0.42x + 2.4 = 0.12x + 3.6$
$0.42x - 0.12x = 3.6 - 2.4$
$0.3x = 1.2$
$x = \frac{1.2}{0.3} = 4$ parts

Answer:

4 parts