For a 14-day camp, sufficient supplies are available for 300 people. 50 more people arrive on day I itself. For how many days will these supplies be sufficient for all these people?

Options

A. 12
B. 11
C. 10
D. 13

Answer

To solve the problem, we need to determine how many days the supplies will last when the number of people increases from 300 to 350 (due to the arrival of 50 additional people).

### Step-by-Step Solution:

1. **Calculate Total Supplies Available**:
- The supplies are sufficient for 300 people for 14 days.
- Therefore, the total amount of supplies can be calculated as:
\[ \text{Total Supplies} = 300 \text{ people} \times 14 \text{ days} = 4200 \text{ person-days} \]

2. **Calculate New Daily Requirement**:
- With the arrival of 50 more people, the total number of people becomes:
\[ 300 + 50 = 350 \text{ people} \]

3. **Determine How Many Days Supplies Last**:
- Now, we need to find out how many days the total supplies (4200 person-days) will last for 350 people.
- Let \( x \) be the number of days the supplies will last. The equation can be set up as:
\[ 350 \text{ people} \times x \text{ days} = 4200 \text{ person-days} \]

4. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = \frac{4200 \text{ person-days}}{350 \text{ people}} = 12 \text{ days} \]

### Conclusion:
The supplies will be sufficient for **12 days** for all 350 people.