If 10 men complete half work in 12 days when they work 8 hours per day, In how many days 18 men complete the full when they work 6 hours/day ?

Answer

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

### Step 1: Understand the given information
We know that:
- 10 men complete half of the work in 12 days while working 8 hours per day.

### Step 2: Calculate the total work in terms of man-hours
Since 10 men complete half of the work in 12 days working 8 hours per day, we can calculate the total man-hours required for half the work:
\[ \text{Total man-hours for half work} = \text{Number of men} \times \text{Number of days} \times \text{Hours per day} \]
\[ = 10 \text{ men} \times 12 \text{ days} \times 8 \text{ hours/day} = 960 \text{ man-hours} \]

Since this is half the work, the total work (W) is:
\[ W = 2 \times 960 = 1920 \text{ man-hours} \]

### Step 3: Set up the equation for the second scenario
Now we need to find out how many days (d2) it will take for 18 men to complete the full work (1920 man-hours) when they work 6 hours per day.

Using the formula:
\[ \text{Total work} = \text{Number of men} \times \text{Number of days} \times \text{Hours per day} \]
We can express this as:
\[ 1920 = 18 \text{ men} \times d2 \times 6 \text{ hours/day} \]

### Step 4: Solve for d2
Rearranging the equation to solve for d2:
\[ d2 = \frac{1920}{18 \times 6} \]
Calculating the denominator:
\[ 18 \times 6 = 108 \]
Now substituting back:
\[ d2 = \frac{1920}{108} \]

### Step 5: Simplify the fraction
To simplify:
\[ d2 = \frac{1920 \div 36}{108 \div 36} = \frac{53.33}{3} \approx 17.78 \]

Thus, the number of days required for 18 men to complete the full work is approximately 17.78 days.

### Final Answer:
**Approximately 17.78 days.**

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