The production cost of Item A is 20% less than the base manufacturing cost of a benchmark model, while the production cost of Item B is 50% more than the base manufacturing cost of the same benchmark model. What is the ratio of the production cost of Item A to that of Item B?

The correct option is 8 : 15.

Step-by-step Explanation:

Let the base manufacturing cost of the benchmark model be $x$.

Step 1: Find the production cost of Item A
The production cost of Item A is 20% less than the base manufacturing cost $x$.
$\text{Cost of Item A}=x-20\%\text{of}x$
$\text{Cost of Item A}=x-0.20x=0.80x$

Step 2: Find the production cost of Item B
The production cost of Item B is 50% more than the base manufacturing cost $x$.
$\text{Cost of Item B}=x+50\%\text{of}x$
$\text{Cost of Item B}=x+0.50x=1.50x$

Step 3: Calculate the ratio of the production cost of Item A to Item B
$\text{Ratio}=\frac{\text{Cost of Item A}}{\text{Cost of Item B}}=\frac{0.80x}{1.50x}$
Simplifying the fraction:
$\text{Ratio}=\frac{0.80}{1.50}=\frac{80}{150}=\frac{8}{15}$

Therefore, the ratio of the production cost of Item A to that of Item B is 8 : 15.