3 persons can build a wall in 4 days, then 4 persons can build it in

Options

A. `5(1)/(3)` days
B. 3 days
C. `4(1)/(3)` days
D. non of these

Answer

To solve the problem step by step, we will use the concept of inverse proportion.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that 3 persons can build a wall in 4 days. We need to find out how many days it will take for 4 persons to build the same wall.

2. **Identifying Variables**:
- Let the number of persons be represented as \( P \).
- Let the number of days taken to complete the wall be represented as \( D \).

3. **Setting Up the Inverse Proportion**:
Since more persons will take less time to complete the wall, we can say that the number of persons and the number of days are inversely proportional. This means:
\[ P_1 \times D_1 = P_2 \times D_2 \]
where:
- \( P_1 = 3 \) (initial number of persons)
- \( D_1 = 4 \) (initial number of days)
- \( P_2 = 4 \) (new number of persons)
- \( D_2 = ? \) (new number of days)

4. **Substituting the Values**:
Plugging the known values into the equation:
\[ 3 \times 4 = 4 \times D_2 \]

5. **Calculating**:
Simplifying the left side:
\[ 12 = 4 \times D_2 \]
Now, divide both sides by 4 to solve for \( D_2 \):
\[ D_2 = \frac{12}{4} = 3 \]

6. **Conclusion**:
Therefore, 4 persons can build the wall in **3 days**.

### Final Answer:
4 persons can build the wall in **3 days**.

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