A military camp has enough food to feed 1000 soldiers for 36 days. If 500 additional soldiers join the camp, then how long will the food last ?

Options

A. 21 days
B. 22 days
C. 23 days
D. 24 days

Answer

To solve the problem, we will use the concept of "man-days," which is the total amount of food available measured in terms of how many soldiers can be fed for how many days.

### Step-by-Step Solution:

1. **Calculate the total food available in man-days:**
- The camp has enough food to feed 1000 soldiers for 36 days.
- Total food in man-days = Number of soldiers × Number of days
- Total food = 1000 soldiers × 36 days = 36,000 man-days

2. **Determine the new number of soldiers:**
- Initially, there are 1000 soldiers.
- 500 additional soldiers join, making the total number of soldiers = 1000 + 500 = 1500 soldiers.

3. **Calculate how long the food will last for the new number of soldiers:**
- Let the number of days the food will last be \( x \).
- The total food available is still 36,000 man-days.
- For 1500 soldiers, the equation becomes:
\[ 1500 \text{ soldiers} \times x \text{ days} = 36,000 \text{ man-days} \]

4. **Solve for \( x \):**
- Rearranging the equation gives:
\[ x = \frac{36,000 \text{ man-days}}{1500 \text{ soldiers}} = 24 \text{ days} \]

5. **Conclusion:**
- The food will last for 24 days with the additional soldiers.

### Final Answer:
The food will last for **24 days**.

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