15 men take 20 days to com plete a job working 8 hours a day. The number of hours a day should 20 men take to complete the job in 12 days

Options

A. 5 hours
B. 10 hours
C. 15 hours
D. 18 hours

Answer

To solve the problem step by step, we will use the relationship between men, days, hours, and work done.

### Step 1: Calculate the total work done in man-hours.
We know that:
- 15 men take 20 days working 8 hours a day.

Total work done (in man-hours) can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]
Substituting the values:
\[ \text{Total Work} = 15 \text{ men} \times 20 \text{ days} \times 8 \text{ hours/day} = 2400 \text{ man-hours} \]

### Step 2: Set up the equation for the new scenario.
Now we need to find out how many hours a day (let's call this \( h_2 \)) 20 men should work to complete the same job in 12 days.

Using the same formula for work:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]
For the new scenario:
\[ 2400 \text{ man-hours} = 20 \text{ men} \times 12 \text{ days} \times h_2 \text{ hours/day} \]

### Step 3: Solve for \( h_2 \).
Now we can set up the equation:
\[ 2400 = 20 \times 12 \times h_2 \]
Calculating the right side:
\[ 2400 = 240 \times h_2 \]
Now, divide both sides by 240 to isolate \( h_2 \):
\[ h_2 = \frac{2400}{240} = 10 \text{ hours} \]

### Conclusion:
Thus, 20 men should work **10 hours a day** to complete the job in 12 days.

---