A team of 30 men is supposed to do a work in 38 days. After 25 days, 5 more men were employed and the work finished one day earlier.How many days would it have been delayed if 5 more men were not employed?

Answer

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

### Step 1: Calculate the total work in man-days
The total work required can be calculated by multiplying the number of men by the number of days they are supposed to work.

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} = 30 \text{ men} \times 38 \text{ days} = 1140 \text{ man-days} \]

### Step 2: Calculate the work done in the first 25 days
In the first 25 days, the 30 men would have completed:

\[ \text{Work done in 25 days} = 30 \text{ men} \times 25 \text{ days} = 750 \text{ man-days} \]

### Step 3: Calculate the remaining work
The remaining work after 25 days is:

\[ \text{Remaining work} = \text{Total work} - \text{Work done in 25 days} = 1140 \text{ man-days} - 750 \text{ man-days} = 390 \text{ man-days} \]

### Step 4: Calculate the number of men after 25 days
After 25 days, 5 more men were employed, making the total number of men:

\[ \text{Total men after 25 days} = 30 + 5 = 35 \text{ men} \]

### Step 5: Calculate the time taken to finish the remaining work with 35 men
Now, we need to find out how many days it takes for 35 men to complete the remaining 390 man-days of work:

\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Number of men}} = \frac{390 \text{ man-days}}{35 \text{ men}} \approx 11.14 \text{ days} \]

Since the work finished one day earlier than the planned 38 days, it means they actually took:

\[ 38 - 1 = 37 \text{ days} \]

### Step 6: Calculate the total days taken without the additional men
If the additional 5 men were not employed, the remaining work would have to be done by the original 30 men. We calculate how many days it would take for 30 men to finish the remaining 390 man-days:

\[ \text{Days required without extra men} = \frac{390 \text{ man-days}}{30 \text{ men}} = 13 \text{ days} \]

### Step 7: Calculate the total days taken without the additional men
If they had taken 13 days to finish the remaining work after the initial 25 days, the total days taken would be:

\[ \text{Total days without extra men} = 25 + 13 = 38 \text{ days} \]

### Step 8: Calculate the delay
Now, we compare this with the original plan of 38 days. Since they finished in 38 days without the additional men, there would be no delay.

### Conclusion
If 5 more men were not employed, the work would not have been delayed.