10 men can make a wall in 8 days. How many men required to complete the same work in half day

Options

A. 80
B. 100
C. 120
D. 160

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the given information
We know that 10 men can complete the work of making a wall in 8 days.

### Step 2: Calculate the total work in man-days
Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 10 \text{ men} \times 8 \text{ days} = 80 \text{ man-days} \]

### Step 3: Determine the time frame for the new scenario
We need to find out how many men are required to complete the same work (80 man-days) in half a day.

### Step 4: Set up the equation for the new scenario
Let \( x \) be the number of men required to complete the work in half a day. The total work done by \( x \) men in half a day can be expressed as:
\[ \text{Work} = x \text{ men} \times 0.5 \text{ days} = 0.5x \text{ man-days} \]

### Step 5: Equate the total work from both scenarios
Since the total work remains the same, we can set up the equation:
\[ 80 \text{ man-days} = 0.5x \text{ man-days} \]

### Step 6: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ 0.5x = 80 \]
\[ x = \frac{80}{0.5} = 80 \times 2 = 160 \]

### Conclusion
Thus, the number of men required to complete the work in half a day is \( \boxed{160} \).

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