Sixty-four men working 8 h a day plan to complete a piece of work in 9 days. However, 5 days later they found that they had completed only 40% of the work. They now wanted to finish the remaining portion of the work in 4 days. How many hours per day should they need to work in order to achieve the target?

Options

A. 11
B. 12
C. 13
D. 15

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total work
Assume the total work to be 100 units.

### Step 2: Calculate the work done in 5 days
The total number of men is 64, and they work 8 hours a day for 5 days.
- Work done in 5 days = Number of men × Hours per day × Days worked
- Work done = 64 men × 8 hours/day × 5 days = 2560 man-hours

### Step 3: Calculate the percentage of work completed
According to the problem, they completed 40% of the work in 5 days.
- Work completed = 40% of 100 = 40 units

### Step 4: Calculate the work rate
Since they completed 40 units in 2560 man-hours, we can find the work rate.
- Work rate = Total work completed / Total man-hours = 40 units / 2560 man-hours = 0.015625 units/man-hour

### Step 5: Calculate the remaining work
The remaining work is:
- Remaining work = Total work - Work completed = 100 - 40 = 60 units

### Step 6: Calculate the total man-hours needed to complete the remaining work
To find out how many man-hours are needed to complete the remaining 60 units:
- Total man-hours needed = Remaining work / Work rate = 60 units / 0.015625 units/man-hour = 3840 man-hours

### Step 7: Calculate the daily work hours required to finish the remaining work in 4 days
Now, they want to complete the remaining work in 4 days. Let \( H \) be the number of hours they need to work per day.
- Total man-hours = Number of men × Hours per day × Days = 64 men × H hours/day × 4 days
- Setting this equal to the total man-hours needed:
\[ 64 \times H \times 4 = 3840 \]

### Step 8: Solve for \( H \)
\[ 256H = 3840 \]
\[ H = \frac{3840}{256} = 15 \]

### Conclusion
The number of hours per day they need to work to complete the remaining work in 4 days is **15 hours**.

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