Throughput accounting ratio

Dear Sir,
I have a question about the TAP

This is the exercise
Unit produced 500
Time taken 200 h
Maxim time available 200h
Material purchase 1000kg costing 3000 $
Labour cost 2000$
Overheads 1500$
Sales 9000$
What is the throughput accounting ratio for this product?

The solution given is the following
Throughput 9000-3000=6000 (this is clear, we have used material purchased instead of used because we suppose no inventory)
Total factory cost 2000+1500=3500
TA ratio = 6000/3500=1.7
This is my question. TA ratio should be calculated as
return per factory hour/cost per factory hour

In the example we have not calculated these ratios and if I try to do it, I don’t get the same solution

Same in this example
The capacity is restrictted by process alpha. Process alpha is expected to be operational for 8h per day and can produce 1200 unit of x per h, 1500 unit of y per h and 600 units of z per hour

Product Througput contribution
X 80
Y 80
Z 200
Conversation cost are 720000$
A change in factory cost arose giving a new figure for conversion cost per factory hour of 80000$. What is the revised TPAR for each product

Also here the calculation is done in this way
TAR= throughput contribution per factory hour/conversion cost per factory hour
Product thougput contrbution Cost factory h
X 80$*(60/0.05)=96,000$ 80,000$
Y 80$*(60/0.04)=120,000$ 80,000$
Z 1200$*(60/0.10)=120,000$ 80,000$

TAP
X =1.2
Y=1.5
Z=1.5

Also here i don’t understand how the TAP is calculated and why i cannot get the same solution if I try to calculate it with the formula

Tap = return per factory hour/cost per factory hour
Can TAP be calculated in 2 different ways?

Thanks