To solve the problem of how long the provisions lasted for 375 men when originally planned for 425 men for 30 days, we can use the concept of inverse proportion. When the number of men decreases, the provisions will last longer. The relationship can be described as:

\(\text{Men}_1 \times \text{Days}_1 = \text{Men}_2 \times \text{Days}_2\)

Where:

• \(\text{Men}_1 = 425\) (initial number of men)
• \(\text{Days}_1 = 30\) (initial number of days the provisions last)
• \(\text{Men}_2 = 375\) (actual number of men)
• \(\text{Days}_2 = ?\) (number of days we need to find)

Substituting the known values into the formula, we get:

\(425 \times 30 = 375 \times \text{Days}_2\)

Solving for \(\text{Days}_2\):

\(\text{Days}_2 = \frac{425 \times 30}{375}\)

Calculating the above expression:

\(\text{Days}_2 = \frac{12750}{375} = 34\)

Thus, the provisions lasted for 34 days for 375 men.

Therefore, the correct answer is 34 days, which corresponds to the given option 34 days.

Understanding this problem involves recognizing that with fewer men, the provisions will last longer, hence the application of inverse proportionality.