38 men can complete a work by working 6 Hrs per day in 12 days then calculate in how many days 51 men can do double of the work by work ing 8 hrs per day?

Options

A. 56 days
B. `(228)/(17)` days
C. 14 days
D. `(128)/(17)` days

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total work done by 38 men in 12 days working 6 hours a day.

Total work (W) can be calculated using the formula:
\[ W = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
Here, we have:
- Number of Men (M1) = 38
- Hours per Day (H1) = 6
- Number of Days (D1) = 12

So,
\[ W = 38 \times 6 \times 12 \]

### Step 2: Calculate the total work.

Calculating the total work:
\[ W = 38 \times 6 = 228 \]
\[ W = 228 \times 12 = 2736 \text{ hours} \]

### Step 3: Since we need to find out how many days 51 men can do double the work, we first calculate double the work.

Double the work (W2) is:
\[ W2 = 2 \times W = 2 \times 2736 = 5472 \text{ hours} \]

### Step 4: Calculate how many days it will take for 51 men working 8 hours a day to complete double the work.

Using the formula for work again:
\[ W2 = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
Let D2 be the number of days required. We have:
- Number of Men (M2) = 51
- Hours per Day (H2) = 8

So,
\[ 5472 = 51 \times 8 \times D2 \]

### Step 5: Rearranging the equation to find D2.

Rearranging gives us:
\[ D2 = \frac{5472}{51 \times 8} \]

### Step 6: Calculate the value of D2.

Calculating the denominator:
\[ 51 \times 8 = 408 \]
Now substituting back:
\[ D2 = \frac{5472}{408} \]

### Step 7: Simplifying the fraction.

Calculating:
\[ D2 = 13.4 \text{ days} \]

### Final Answer:
Thus, it will take approximately 13.4 days for 51 men to complete double the work working 8 hours a day.

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