Working 7 hours in a day, 4 men can do a piece of work in 8 days. Working 8 hours in a day, the required number of men to perform the same work in 4 days will be

Options

A. 1. 8
B. 2. 4
C. 3. 7
D. 4. 9

Answer

To solve the problem step by step, we can use the formula that relates the number of men, days, and hours worked. The formula is:

\[ m_1 \times d_1 \times h_1 = m_2 \times d_2 \times h_2 \]

Where:
- \( m_1 \) = number of men in the first scenario
- \( d_1 \) = number of days in the first scenario
- \( h_1 \) = number of hours worked per day in the first scenario
- \( m_2 \) = number of men in the second scenario (which we need to find)
- \( d_2 \) = number of days in the second scenario
- \( h_2 \) = number of hours worked per day in the second scenario

### Step 1: Identify the values from the first scenario
From the question, we know:
- \( m_1 = 4 \) (4 men)
- \( d_1 = 8 \) (8 days)
- \( h_1 = 7 \) (7 hours per day)

### Step 2: Identify the values from the second scenario
For the second scenario, we have:
- \( d_2 = 4 \) (4 days)
- \( h_2 = 8 \) (8 hours per day)
- \( m_2 = ? \) (we need to find this)

### Step 3: Set up the equation
Using the formula, we can set up the equation as follows:

\[ 4 \times 8 \times 7 = m_2 \times 4 \times 8 \]

### Step 4: Simplify the equation
We can simplify both sides of the equation. First, notice that \( 4 \) and \( 8 \) on both sides can be canceled out:

\[ 4 \times 7 = m_2 \]

### Step 5: Calculate \( m_2 \)
Now, we calculate \( m_2 \):

\[ m_2 = 4 \times 7 = 28 \]

### Conclusion
Thus, the required number of men to perform the same work in 4 days working 8 hours a day is **28 men**.