If 40 persons can do a piece of work in 14 days, then the number of persons required to complete the work in 28 days.

Options

A. 40
B. 20
C. 14
D. 10

Answer

To solve the problem, we need to determine how many persons are required to complete the same piece of work in 28 days, given that 40 persons can complete it in 14 days.

### Step-by-Step Solution:

1. **Calculate the Total Work Done in Person-Days:**
The total work can be calculated in terms of person-days. If 40 persons can complete the work in 14 days, we can find the total work in person-days as follows:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} = 40 \times 14 = 560 \text{ person-days} \]

2. **Determine the Number of Persons Required for 28 Days:**
Now, we want to find out how many persons (let's denote this as \( x \)) are needed to complete the same work in 28 days. We can set up the equation:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} \]
Substituting the known values:
\[ 560 = x \times 28 \]

3. **Solve for \( x \):**
To find \( x \), we can rearrange the equation:
\[ x = \frac{560}{28} \]
Now, perform the division:
\[ x = 20 \]

Thus, the number of persons required to complete the work in 28 days is **20**.

### Final Answer:
The number of persons required to complete the work in 28 days is **20**.

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