In a fort, 360 men had provisions for 21 days. If 60 more men join them, how long will the provisions last?

Answer

To solve the problem step by step, we can use the concept of the Unitary Method.

### Step 1: Understand the initial situation
Initially, we have 360 men who have provisions for 21 days.

### Step 2: Calculate the total amount of provisions
To find the total amount of provisions available, we can calculate it as follows:
- Total provisions = Number of men × Number of days
- Total provisions = 360 men × 21 days = 7560 man-days

### Step 3: Determine the new number of men
Now, if 60 more men join, the total number of men becomes:
- Total men = 360 men + 60 men = 420 men

### Step 4: Set up the equation for the new situation
Let \( x \) be the number of days the provisions will last for 420 men. The total provisions remain the same, so we can set up the equation:
- Total provisions = Number of men × Number of days
- 7560 man-days = 420 men × \( x \) days

### Step 5: Solve for \( x \)
Now we can solve for \( x \):
\[ x = \frac{7560 \text{ man-days}}{420 \text{ men}} = 18 \text{ days} \]

### Conclusion
Therefore, the provisions will last for **18 days** with the additional 60 men.

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