15 men can build a 16.5 m long wall in one day. How many men are required to build 66 m long wall in one day?

Answer

To solve the problem step by step, we will use the relationship between the number of men, the days worked, and the work done.

### Step 1: Understand the given information
We know that:
- 15 men can build a 16.5 m long wall in 1 day.
- We need to find out how many men (let's call this \( m_2 \)) are required to build a 66 m long wall in 1 day.

### Step 2: Set up the proportion
We can use the formula that relates the number of men, days, and work done:
\[ m_1 \times d_1 \times w_2 = m_2 \times d_2 \times w_1 \]
Where:
- \( m_1 = 15 \) (number of men in the first case)
- \( d_1 = 1 \) (days in the first case)
- \( w_1 = 16.5 \) m (work done in the first case)
- \( w_2 = 66 \) m (work done in the second case)
- \( d_2 = 1 \) (days in the second case)

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation gives us:
\[ 15 \times 1 \times 66 = m_2 \times 1 \times 16.5 \]

### Step 4: Simplify the equation
This simplifies to:
\[ 15 \times 66 = m_2 \times 16.5 \]

### Step 5: Calculate \( 15 \times 66 \)
Calculating \( 15 \times 66 \):
\[ 15 \times 66 = 990 \]

### Step 6: Set up the equation to find \( m_2 \)
Now we have:
\[ 990 = m_2 \times 16.5 \]

### Step 7: Solve for \( m_2 \)
To find \( m_2 \), we divide both sides by 16.5:
\[ m_2 = \frac{990}{16.5} \]

### Step 8: Perform the division
Calculating \( \frac{990}{16.5} \):
\[ m_2 = 60 \]

### Conclusion
Therefore, the number of men required to build a 66 m long wall in one day is **60 men**.

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