If 28 men working 8 hours per day can finish a piece of work in 10 days. How many hours per day 40 men must work to complete the same work in 8 days.

Options

A. 6 hours
B. (6)1/2 hours
C. 7 hours
D. 9 hours

Answer

To solve the problem, we will first determine the total amount of work done in terms of man-hours and then find out how many hours per day 40 men need to work to complete the same amount of work in 8 days.

### Step 1: Calculate the total work done by 28 men in 10 days.

The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]

Substituting the values:
\[ \text{Total Work} = 28 \text{ men} \times 8 \text{ hours/day} \times 10 \text{ days} \]
\[ \text{Total Work} = 28 \times 8 \times 10 = 2240 \text{ man-hours} \]

### Step 2: Set up the equation for 40 men working for 8 days.

Let \( x \) be the number of hours per day that 40 men need to work. The total work done by 40 men in 8 days can be expressed as:
\[ \text{Total Work} = 40 \text{ men} \times x \text{ hours/day} \times 8 \text{ days} \]
\[ \text{Total Work} = 320x \text{ man-hours} \]

### Step 3: Equate the total work from both scenarios.

Since both scenarios complete the same amount of work, we can set the equations equal to each other:
\[ 2240 = 320x \]

### Step 4: Solve for \( x \).

To find \( x \), divide both sides by 320:
\[ x = \frac{2240}{320} \]
\[ x = 7 \]

### Conclusion:

Thus, 40 men must work **7 hours per day** to complete the same work in 8 days.

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