A contract is to be completed in 75 days and 187 men are to work 15 hours per day. After 65 days, 3/5 of the work is completed. How many additional men may be employed, so that the work may be completed in time each man now working 17 hours per day?

Options

A. 495
B. 514
C. 528
D. 532

Answer

To solve the problem step by step, we will break down the information given and calculate the required values.

### Step 1: Understand the total work and the initial conditions
- Total days to complete the work = 75 days
- Number of men initially employed = 187 men
- Hours worked per day by each man = 15 hours

### Step 2: Calculate the total work in man-hours
Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Total Days} \]
\[ \text{Total Work} = 187 \times 15 \times 75 \]
Calculating this gives:
\[ \text{Total Work} = 187 \times 15 = 2805 \text{ man-hours} \]
\[ \text{Total Work} = 2805 \times 75 = 210375 \text{ man-hours} \]

### Step 3: Calculate the work completed in 65 days
After 65 days, it is given that \( \frac{3}{5} \) of the work is completed. Therefore, the work done is:
\[ \text{Work Done} = \frac{3}{5} \times \text{Total Work} \]
Calculating this gives:
\[ \text{Work Done} = \frac{3}{5} \times 210375 = 126225 \text{ man-hours} \]

### Step 4: Calculate the remaining work
The remaining work to be completed is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done} \]
Calculating this gives:
\[ \text{Remaining Work} = 210375 - 126225 = 84150 \text{ man-hours} \]

### Step 5: Calculate the time left to complete the remaining work
The time left to complete the work is:
\[ \text{Time Left} = 75 - 65 = 10 \text{ days} \]

### Step 6: Calculate the total man-hours available with the new working hours
Each man now works 17 hours per day. Therefore, the total man-hours available with the current workforce (187 men) in the remaining 10 days is:
\[ \text{Available Man-Hours} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days Left} \]
Calculating this gives:
\[ \text{Available Man-Hours} = 187 \times 17 \times 10 = 31790 \text{ man-hours} \]

### Step 7: Calculate the additional man-hours required
The additional man-hours required to complete the remaining work is:
\[ \text{Additional Man-Hours Required} = \text{Remaining Work} - \text{Available Man-Hours} \]
Calculating this gives:
\[ \text{Additional Man-Hours Required} = 84150 - 31790 = 52360 \text{ man-hours} \]

### Step 8: Calculate the number of additional men needed
Let \( x \) be the number of additional men required. Each man will work 17 hours per day for 10 days, so:
\[ x \times 17 \times 10 = 52360 \]
\[ x \times 170 = 52360 \]
\[ x = \frac{52360}{170} = 308 \]

### Step 9: Calculate the total number of men required
The total number of men required is:
\[ \text{Total Men} = \text{Initial Men} + \text{Additional Men} = 187 + 308 = 495 \]

### Step 10: Conclusion
Thus, the number of additional men that may be employed is:
\[ \text{Additional Men} = 308 \]