To solve this problem, we can use the concept of inverse proportionality. Let's denote the number of workers as "w" and the number of days required for renovation as "d."
According to the problem, we have the following information: When 6 workers are doing the job (w = 6), the renovation takes 8 days (d = 8).
We can set up the proportionality equation as follows:
w1 × d1 = w2 × d2
where w1 = 6, d1 = 8 (when 6 workers complete the job in 8 days), and d2 = 12 (when we want to find the number of workers, w2).
Plugging in the values:
6 × 8 = w2 × 12
48 = 12w2
Now, we can solve for w2 by dividing both sides of the equation by 12:
48/12 = w2
4 = w2
Therefore, to complete the job in 12 days, we would need 4 workers.