To solve this, we use the concept of man-days, which means that the total amount of work done is the same, regardless of how many workers are involved, as long as the total man-days are the same.

The total amount of work is:

$\text{Work} = \text{Number of men} \times \text{Number of days}$

For the first case, the total work can be expressed as:

$\text{Work} = 42 \text{ men} \times 15 \text{ days} = 630 \text{ man-days}$

Now, we want to find how many days it will take for 30 men to complete the same work. Let $x$ be the number of days for 30 men:

$\text{Work} = 30 \text{ men} \times x \text{ days} = 630 \text{ man-days}$

Now solve for $x$:

$30x = 630$

$x = \frac{630}{30} = 21 \text{ days}$

Thus, it will take 21 days for 30 men to complete the same work.

Would you like further details on this or have any other questions?

Here are 5 related questions:

1. If 42 men took 10 days to complete the work, how long would 28 men take?
2. If 15 men can complete a work in 20 days, how many men are needed to finish it in 10 days?
3. If 30 men can complete a work in 21 days, how long would 60 men take to complete the same work?
4. What if 42 men work for half a day every day? How many days would it take to finish the work?
5. How would the completion time change if one worker becomes twice as efficient?

Tip: Always check the proportion of workers and days in such problems; they are inversely related!