Twelve men, working at 8 h a day, can do a piece of work in 18 days. In how many days can 24 men working at 6 h a day can do the same work?

Options

A. 12
B. 16
C. 20
D. 30

Explanation

To solve the problem step by step, we will use the concept of work done, which is calculated as the product of the number of men, the number of hours they work per day, and the number of days they work.

### Step 1: Calculate the total work done in terms of man-hours
We know that:
- 12 men work for 8 hours a day for 18 days.

The total work done (in man-hours) can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days} \]
Substituting the given values:
\[ \text{Total Work} = 12 \times 8 \times 18 \]

### Step 2: Calculate the total work
Now, let's calculate the total work:
\[ 12 \times 8 = 96 \quad \text{(man-hours per day)} \]
\[ 96 \times 18 = 1728 \quad \text{(total man-hours)} \]

### Step 3: Set up the equation for the second scenario
Now we need to find out how many days (let's call it \(d_2\)) it will take for 24 men working 6 hours a day to complete the same amount of work (1728 man-hours).

Using the same formula for work:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days} \]
For the second scenario:
\[ 1728 = 24 \times 6 \times d_2 \]

### Step 4: Calculate the work done by 24 men in 6 hours
Calculating the work done by 24 men in 6 hours:
\[ 24 \times 6 = 144 \quad \text{(man-hours per day)} \]

### Step 5: Set up the equation to solve for \(d_2\)
Now we can substitute this back into our equation:
\[ 1728 = 144 \times d_2 \]

### Step 6: Solve for \(d_2\)
To find \(d_2\), divide both sides by 144:
\[ d_2 = \frac{1728}{144} \]

### Step 7: Calculate \(d_2\)
Calculating \(d_2\):
\[ d_2 = 12 \]

### Final Answer
Thus, 24 men working 6 hours a day can complete the same work in **12 days**.

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