In an army camp, there were provisions for 425 men for 30 days. How long did the provisions last for 375 men?

Answer

To solve the problem, we will use the concept of direct proportion. The total amount of provisions is constant, so if the number of men decreases, the number of days the provisions last will increase.

### Step-by-Step Solution:

1. **Identify the given information**:
- Provisions for 425 men last for 30 days.
- We need to find out how long the provisions will last for 375 men.

2. **Set up the relationship**:
- We know that the total provisions can be expressed as the product of the number of men and the number of days they last.
- For 425 men, the total provisions can be calculated as:
\[ \text{Total provisions} = 425 \text{ men} \times 30 \text{ days} \]

3. **Calculate the total provisions**:
- Calculate the total provisions:
\[ \text{Total provisions} = 425 \times 30 = 12750 \text{ man-days} \]

4. **Set up the equation for 375 men**:
- Let \( X \) be the number of days the provisions will last for 375 men.
- The total provisions can also be expressed as:
\[ \text{Total provisions} = 375 \text{ men} \times X \text{ days} \]

5. **Equate the two expressions for total provisions**:
- Setting the two expressions for total provisions equal gives us:
\[ 425 \times 30 = 375 \times X \]

6. **Substitute the total provisions**:
- Substitute the value we calculated for total provisions:
\[ 12750 = 375 \times X \]

7. **Solve for \( X \)**:
- To find \( X \), divide both sides by 375:
\[ X = \frac{12750}{375} \]

8. **Calculate \( X \)**:
- Performing the division:
\[ X = 34 \]

9. **Conclusion**:
- Therefore, the provisions will last for **34 days** for 375 men.