If 900 persons can finish the construction of a building in 40 days, how many persons are needed to complete the construction of building in 25 days.

Answer

To solve the problem step by step, we can use the concept of direct proportion. The formula we will use is:

\[ \frac{m_1 \cdot d_1}{w_1} = \frac{m_2 \cdot d_2}{w_2} \]

Where:
- \(m\) = number of persons
- \(d\) = number of days
- \(w\) = work done (which remains constant in this case)

### Step 1: Identify the known values
From the question:
- \(m_1 = 900\) (the number of persons)
- \(d_1 = 40\) (the number of days)
- \(d_2 = 25\) (the new number of days)
- \(m_2 = x\) (the number of persons we need to find)

### Step 2: Set up the equation
Since the work done \(w\) is the same in both cases, we can ignore it in our calculations. Thus, we can set up the equation as follows:

\[ \frac{900 \cdot 40}{w} = \frac{x \cdot 25}{w} \]

### Step 3: Cancel out \(w\)
Since \(w\) is the same on both sides, we can cancel it out:

\[ 900 \cdot 40 = x \cdot 25 \]

### Step 4: Solve for \(x\)
Now we can solve for \(x\):

\[ x = \frac{900 \cdot 40}{25} \]

### Step 5: Simplify the expression
Now, simplify the right side:

1. Calculate \(900 \cdot 40\):
\[ 900 \cdot 40 = 36000 \]

2. Now divide by 25:
\[ x = \frac{36000}{25} \]

3. Perform the division:
\[ x = 1440 \]

### Conclusion
Thus, the number of persons needed to complete the construction of the building in 25 days is **1440**.

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