15 persons can fill 35 boxes in 7 days. How many Persons can fill 65 boxes in 5 days?

Options

A. 13
B. 39
C. 45
D. 65

Answer

To solve the problem, we can use the concept of work done, which relates the number of persons, the number of boxes, and the number of days.

### Step-by-Step Solution:

1. **Identify the given information:**
- 15 persons can fill 35 boxes in 7 days.
- We need to find out how many persons (let's call it \( M_2 \)) are required to fill 65 boxes in 5 days.

2. **Calculate the total work done in terms of person-days for the first scenario:**
- Total work done (in person-days) = Number of persons × Number of days
- For the first scenario:
\[ \text{Work}_1 = 15 \text{ persons} \times 7 \text{ days} = 105 \text{ person-days} \]
- This means that 105 person-days are required to fill 35 boxes.

3. **Calculate the work done per box:**
- Work done per box = Total work / Number of boxes
- For the first scenario:
\[ \text{Work per box} = \frac{105 \text{ person-days}}{35 \text{ boxes}} = 3 \text{ person-days per box} \]

4. **Calculate the total work required for the second scenario (65 boxes):**
- Total work required for 65 boxes:
\[ \text{Work}_2 = 65 \text{ boxes} \times 3 \text{ person-days per box} = 195 \text{ person-days} \]

5. **Set up the equation for the second scenario:**
- We know that in the second scenario, the work done is equal to the number of persons multiplied by the number of days:
\[ M_2 \times 5 \text{ days} = 195 \text{ person-days} \]

6. **Solve for \( M_2 \):**
- Rearranging the equation gives:
\[ M_2 = \frac{195 \text{ person-days}}{5 \text{ days}} = 39 \text{ persons} \]

### Final Answer:
Thus, the number of persons required to fill 65 boxes in 5 days is **39 persons**.