10 men can finish the construction of a wall in 8 days.How many men are added to finish the work in half a day ?

Options

A. 80
B. 100
C. 120
D. 0.625

Answer

To solve the problem step by step, we will use the concept of the Unitary Method and the idea of indirect proportion.

### Step-by-Step Solution:

1. **Understand the given information**:
- 10 men can finish the construction of a wall in 8 days.

2. **Calculate the total work in man-days**:
- Total work = Number of men × Number of days
- Total work = 10 men × 8 days = 80 man-days.

3. **Determine the required time to finish the work**:
- We need to find out how many men are required to finish the same work in half a day (0.5 days).

4. **Set up the equation using the concept of man-days**:
- Let the number of men required to finish the work in half a day be \( x \).
- Total work = Number of men × Number of days
- Therefore, 80 man-days = \( x \) men × 0.5 days.

5. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = \frac{80 \text{ man-days}}{0.5 \text{ days}} = 80 \div 0.5 = 160 \text{ men}. \]

6. **Calculate how many men are added**:
- We initially had 10 men.
- Men added = Total men required - Initial men
- Men added = 160 men - 10 men = 150 men.

### Final Answer:
150 men need to be added to finish the construction of the wall in half a day.

---