How many days will 1648 persons take to construct a dam, if 721 persons can build the same in 48 days?

Options

A. 21 days
B. 20 days
C. 23 days
D. 24 days

Answer

To solve the problem of how many days 1648 persons will take to construct a dam, given that 721 persons can build the same dam in 48 days, we can follow these steps:

### Step 1: Calculate the total work done in person-days
First, we need to calculate the total work done by 721 persons in 48 days. The total work can be calculated using the formula:

\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} \]

Substituting the values:

\[ \text{Total Work} = 721 \text{ persons} \times 48 \text{ days} = 34568 \text{ person-days} \]

### Step 2: Set up the equation for the new scenario
Now, we need to find out how many days (let's call it \( x \)) it will take for 1648 persons to complete the same amount of work (34568 person-days). We can set up the equation as follows:

\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} \]

Substituting the values for the new scenario:

\[ 34568 \text{ person-days} = 1648 \text{ persons} \times x \text{ days} \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{34568 \text{ person-days}}{1648 \text{ persons}} \]

Calculating this gives:

\[ x = \frac{34568}{1648} \approx 21 \text{ days} \]

### Conclusion
Thus, 1648 persons will take approximately 21 days to construct the dam.