12 persons can do a piece of work in 4 days. How many persons are required to complete 8 times the work in half the time?

Options

A. 192
B. 190
C. 180
D. 144

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial work scenario
We know that 12 persons can complete 1 piece of work in 4 days.

### Step 2: Calculate the total work in person-days
The total work can be calculated in terms of person-days:
- Total work = Number of persons × Number of days
- Total work = 12 persons × 4 days = 48 person-days

### Step 3: Determine the new work scenario
We need to complete 8 times the work in half the time:
- New work = 8 × 1 = 8 pieces of work
- New time = 4 days / 2 = 2 days

### Step 4: Calculate the total work required for the new scenario
Now, we calculate the total work in person-days for the new scenario:
- Total work required = 8 pieces of work × 48 person-days (from Step 2)
- Total work required = 8 × 48 = 384 person-days

### Step 5: Calculate the number of persons required
Now we need to find out how many persons are required to complete 384 person-days of work in 2 days:
- Let the number of persons required be \( P \).
- We know that \( P \) persons working for 2 days should equal the total work required.
- Therefore, \( P × 2 days = 384 person-days \)

### Step 6: Solve for \( P \)
To find \( P \):
- \( P = \frac{384}{2} = 192 \)

### Conclusion
Thus, **192 persons** are required to complete 8 times the work in half the time.

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