40 men can build a wall 200 m long in 12 days, working 8 h a day. What will be the number of days that 30 men will take to build a similar wall 300 m long, working 6 h per day

Options

A. 32
B. 18
C. 36
D. 9

Answer

To solve the problem step-by-step, we will use the formula that relates the number of men (m), days (d), hours per day (h), and work done (w). The formula we will use is:

\[ \frac{m_1 \cdot d_1 \cdot h_1}{w_1} = \frac{m_2 \cdot d_2 \cdot h_2}{w_2} \]

### Step 1: Identify the values from the first case
From the problem, we have the following values for the first case:
- \( m_1 = 40 \) men
- \( d_1 = 12 \) days
- \( h_1 = 8 \) hours/day
- \( w_1 = 200 \) meters (length of the wall)

### Step 2: Identify the values from the second case
For the second case, we have:
- \( m_2 = 30 \) men
- \( d_2 = ? \) (this is what we need to find)
- \( h_2 = 6 \) hours/day
- \( w_2 = 300 \) meters (length of the wall)

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula:

\[ \frac{40 \cdot 12 \cdot 8}{200} = \frac{30 \cdot d_2 \cdot 6}{300} \]

### Step 4: Simplify both sides
First, simplify the left side:

\[ \frac{40 \cdot 12 \cdot 8}{200} = \frac{3840}{200} = 19.2 \]

Now simplify the right side:

\[ \frac{30 \cdot d_2 \cdot 6}{300} = \frac{180d_2}{300} = 0.6d_2 \]

### Step 5: Set the two sides equal to each other
Now we have:

\[ 19.2 = 0.6d_2 \]

### Step 6: Solve for \( d_2 \)
To find \( d_2 \), divide both sides by 0.6:

\[ d_2 = \frac{19.2}{0.6} = 32 \]

### Conclusion
Thus, the number of days that 30 men will take to build a similar wall 300 m long, working 6 hours per day, is **32 days**.

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