Seventy-five men are employed to lay down a railway line in 3 months. Due to certain emergency conditions, the work was to be finished in 18 days. How many more men should be employed to complete the work in the desired time ?

Options

A. 300
B. 325
C. 350
D. 375

Answer

To solve the problem, we will use the concept of man-days, which is a way to measure the amount of work done by a certain number of men in a given number of days.

### Step-by-Step Solution:

1. **Determine the total work in man-days**:
- We know that 75 men can complete the work in 3 months.
- First, convert months to days. Assuming 1 month = 30 days, then 3 months = 3 × 30 = 90 days.
- Therefore, the total work in man-days = Number of men × Number of days = 75 men × 90 days = 6750 man-days.

2. **Calculate the required work to be done in the new time frame**:
- The work needs to be completed in 18 days.
- Let \( M_2 \) be the number of men required to complete the work in 18 days.
- The equation for the total work remains the same: \( M_2 \times 18 \text{ days} = 6750 \text{ man-days} \).

3. **Solve for \( M_2 \)**:
- Rearranging the equation gives us \( M_2 = \frac{6750 \text{ man-days}}{18 \text{ days}} \).
- Calculating this gives \( M_2 = 375 \text{ men} \).

4. **Determine how many more men are needed**:
- Initially, there were 75 men employed.
- The additional men required = Total men required - Initial men = \( 375 - 75 = 300 \).

### Final Answer:
Therefore, **300 more men should be employed** to complete the work in the desired time of 18 days.

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