A road of 5 km length will be con structed in 100 days. So 280 workers were employed. But after 80 days it was found that only `3(1)/(2)` km road was completed. Now how many more people were needed to finish the work in the specified time?

Options

A. 480
B. 80
C. 200
D. 100

Answer

To solve the problem step by step, we will break down the information given and calculate how many more workers are needed to complete the road construction on time.

### Step 1: Understand the problem
- A road of length 5 km is to be constructed in 100 days.
- 280 workers are employed for this task.
- After 80 days, only 3.5 km of the road has been completed.

### Step 2: Calculate the amount of work completed
- Total work required = 5 km
- Work completed in 80 days = 3.5 km
- Work remaining = Total work - Work completed = 5 km - 3.5 km = 1.5 km

### Step 3: Determine the remaining time
- Total time for construction = 100 days
- Time spent = 80 days
- Remaining time = Total time - Time spent = 100 days - 80 days = 20 days

### Step 4: Calculate the work done per day by the current workers
- Work done by 280 workers in 80 days = 3.5 km
- Work done per day = Total work done / Number of days = 3.5 km / 80 days = 0.04375 km/day

### Step 5: Calculate the total work rate needed to finish the remaining work
- Remaining work = 1.5 km
- Time left = 20 days
- Required work rate to finish on time = Remaining work / Remaining time = 1.5 km / 20 days = 0.075 km/day

### Step 6: Calculate the number of workers needed to achieve the required work rate
- Current work rate of 280 workers = 0.04375 km/day
- Work rate per worker = 0.04375 km/day / 280 workers = 0.00015625 km/worker/day
- Required number of workers = Required work rate / Work rate per worker = 0.075 km/day / 0.00015625 km/worker/day

### Step 7: Calculate the required number of workers
- Required number of workers = 0.075 / 0.00015625 = 480 workers

### Step 8: Calculate how many more workers are needed
- Current number of workers = 280
- Additional workers needed = Required workers - Current workers = 480 - 280 = 200 workers

### Final Answer
200 more workers are needed to finish the work in the specified time.

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