If 20 men complete a work in 56 days by working 10 hours a day how many days will 40 men take to complete the same work by working 8 hours a day?

Options

A. 30
B. 25
C. 48
D. 35

Answer

To solve the problem, we will use the concept of man-hours, which is the total amount of work done by a certain number of men over a specific period of time.

### Step-by-Step Solution:

1. **Calculate the total work done in man-hours by the first group:**
- Number of men (M1) = 20
- Number of days (D1) = 56
- Number of hours per day (H1) = 10

Total work (in man-hours) = M1 × D1 × H1
\[ \text{Total work} = 20 \text{ men} \times 56 \text{ days} \times 10 \text{ hours/day} = 11200 \text{ man-hours} \]

2. **Set up the equation for the second group of workers:**
- Number of men (M2) = 40
- Number of hours per day (H2) = 8
- Number of days (D2) = ?

We know the total work remains the same, so we can set up the equation:
\[ M2 \times D2 \times H2 = \text{Total work} \]
Substituting the known values:
\[ 40 \text{ men} \times D2 \times 8 \text{ hours/day} = 11200 \text{ man-hours} \]

3. **Solve for D2:**
\[ 320D2 = 11200 \]
Now, divide both sides by 320:
\[ D2 = \frac{11200}{320} = 35 \text{ days} \]

### Final Answer:
The number of days 40 men will take to complete the same work by working 8 hours a day is **35 days**.

---