In how many days 40 complete the work working 6 hours a day 

To determine the number of days required for 40 men to complete the work while working 6 hours a day, we can use the efficiency ratio calculated earlier. Let's solve it step by step.

### Step 1: Recall the Efficiency of One Man
We have already determined that the work done by 20 men working 5 hours a day for 10 days can be expressed as:

\[
\text{Work done} = 20 \times 10 \times 5 \times E_m = 1000 \times E_m
\]

This is the total work to be done.

### Step 2: Calculate the Work Done by 40 Men Working 6 Hours a Day
If 40 men work 6 hours a day for \( x \) days, the total work done can be expressed as:

\[
\text{Work done} = 40 \times x \times 6 \times E_m = 240x \times E_m
\]

### Step 3: Equate the Two Expressions for Total Work
Since the total work remains the same, we equate the two expressions:

\[
1000 \times E_m = 240x \times E_m
\]

### Step 4: Solve for \( x \)
We can cancel \( E_m \) from both sides:

\[
1000 = 240x
\]

\[
x = \frac{1000}{240} \approx 4.167 \text{ days}
\]

### Conclusion
It will take approximately **4.167 days** (which is about 4 days and 4 hours) for 40 men to complete the work while working 6 hours a day.

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Would you like further clarification on any part of this problem, or do you have additional questions?

Here are five related questions to explore further:

1. How many days would it take 50 men working 7 hours a day to complete the same work?
2. If 30 men worked 8 hours a day, how long would it take to complete the work?
3. What if the number of hours worked per day was reduced to 4 hours? How would this affect the completion time?
4. How would the result change if the efficiency of each man was increased by 20%?
5. What is the impact of adding more workers on the overall completion time?

**Tip:** When dealing with work problems, it's useful to standardize the amount of work done per unit of time, such as man-hours, to simplify calculations.

Discover how long it takes for 40 men to complete a task working 6 hours a day. Use our step-by-step solution for work and time problems, including efficiency ratios and work formulas. Suitable for high school students studying work problems.

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