A fort has provision of 150 men for 35 days. For how many days will it be sufficient for 125 men?

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the relationship between men and days
We know that if the number of men increases, the number of days the food lasts decreases, and vice versa. This means that the number of men (n) and the number of days (d) are inversely proportional.

### Step 2: Set up the equation
Let \( x \) be the number of days the food will last for 125 men. According to the problem:
- For 150 men, the food lasts for 35 days.

Using the relationship of inverse proportionality, we can write:
\[ n_1 \times d_1 = n_2 \times d_2 \]
Where:
- \( n_1 = 150 \) (number of men)
- \( d_1 = 35 \) (number of days)
- \( n_2 = 125 \) (number of men)
- \( d_2 = x \) (number of days for 125 men)

So, we can set up the equation:
\[ 150 \times 35 = 125 \times x \]

### Step 3: Substitute the values into the equation
Now, substituting the known values:
\[ 150 \times 35 = 125 \times x \]

### Step 4: Calculate the left side
Calculate \( 150 \times 35 \):
\[ 150 \times 35 = 5250 \]

### Step 5: Set up the equation for \( x \)
Now we have:
\[ 5250 = 125 \times x \]

### Step 6: Solve for \( x \)
To find \( x \), divide both sides by 125:
\[ x = \frac{5250}{125} \]

### Step 7: Perform the division
Calculating \( \frac{5250}{125} \):
\[ x = 42 \]

### Conclusion
Thus, the food will last for **42 days** for 125 men.