We can use the concept of "man-days" to solve this problem.
"Man-days" represent the total amount of work done by one person in one day.
Given that 40 workers can finish the work in 30 days, the total man-days required are:
\[40 \text{ workers} \times 30 \text{ days} = 1200 \text{ man-days}\]
Now, we can find out how many man-days 120 workers can complete in one day:
\[
\text{Man-days by } 120 \text{ workers} = 120 \text{ workers} \times \text{Number of days}
\]
We need to solve for the number of days:
\[
120 \text{ workers} \times \text{Number of days} = 1200 \text{ man-days}
\]
Divide both sides by 120 workers:
\[
\text{Number of days} = \frac{1200 \text{ man-days}}{120 \text{ workers}} = 10 \text{ days}
\]
So, 120 workers can finish the same work in 10 days.
