10 men working 6 h a day can complete a work in 18 days. How many hours per day must 15 men work to complete the same work in 12 days.

Options

A. 6
B. 10
C. 12
D. none of these

Answer

To solve the problem step by step, we will use the relationship between the number of men, the number of days, the number of hours worked per day, and the efficiency of work done.

### Step 1: Determine the total work done in man-hours.
The total work done can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]

For the first scenario:
- Number of Men (P1) = 10
- Number of Days (D1) = 18
- Number of Hours per Day (H1) = 6

Calculating the total work:
\[ \text{Total Work} = 10 \times 18 \times 6 = 1080 \text{ man-hours} \]

### Step 2: Set up the equation for the second scenario.
In the second scenario, we need to find out how many hours (H2) 15 men must work to complete the same work in 12 days.

For the second scenario:
- Number of Men (P2) = 15
- Number of Days (D2) = 12
- Number of Hours per Day (H2) = ?

Using the same total work formula:
\[ \text{Total Work} = 15 \times 12 \times H2 \]

### Step 3: Equate the total work from both scenarios.
Since the total work done is the same in both scenarios, we can set the equations equal to each other:
\[ 10 \times 18 \times 6 = 15 \times 12 \times H2 \]

Substituting the total work calculated:
\[ 1080 = 15 \times 12 \times H2 \]

### Step 4: Solve for H2.
First, calculate \( 15 \times 12 \):
\[ 15 \times 12 = 180 \]

Now, substitute this back into the equation:
\[ 1080 = 180 \times H2 \]

To find H2, divide both sides by 180:
\[ H2 = \frac{1080}{180} = 6 \]

### Conclusion:
Thus, the number of hours per day that 15 men must work to complete the same work in 12 days is **6 hours**.