A builder decided to build a farmhouse in 45 days. He employed 106 men in the beginning and 53 more after 35 days and completed the construction in stipulated time. If he had not employed the additional men, how many days behing schedule would it have been finished?

Options

A. 5 days
B. 6 days
C. 8 days
D. 10 days

Answer

To solve the problem, we need to determine how many days behind schedule the construction would have been if the builder had not employed the additional 53 men.

### Step-by-Step Solution:

1. **Calculate the total work done in man-days:**
The builder decided to complete the farmhouse in 45 days with 106 men.
\[ \text{Total work} = \text{Number of men} \times \text{Number of days} = 106 \times 45 = 4770 \text{ man-days} \]

2. **Calculate the work done in the first 35 days:**
In the first 35 days, only 106 men were working.
\[ \text{Work done in 35 days} = 106 \times 35 = 3710 \text{ man-days} \]

3. **Calculate the remaining work after 35 days:**
\[ \text{Remaining work} = \text{Total work} - \text{Work done in 35 days} = 4770 - 3710 = 1060 \text{ man-days} \]

4. **Calculate the work done by the additional men:**
After 35 days, the builder employed an additional 53 men, making a total of:
\[ \text{Total men after 35 days} = 106 + 53 = 159 \text{ men} \]
They worked for the remaining 10 days (from day 36 to day 45).
\[ \text{Work done in 10 days} = 159 \times 10 = 1590 \text{ man-days} \]

5. **Verify the total work done:**
The total work done in 45 days is:
\[ \text{Total work done} = \text{Work done in first 35 days} + \text{Work done in last 10 days} = 3710 + 1590 = 5300 \text{ man-days} \]
However, since we calculated the total work required as 4770 man-days, we see that the additional men allowed the work to be completed on time.

6. **Calculate how long it would take without the additional men:**
If the builder had not employed the additional 53 men, the remaining work of 1060 man-days would have to be completed by the original 106 men.
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Number of men}} = \frac{1060}{106} = 10 \text{ days} \]

7. **Calculate the total days taken without additional men:**
If the original 106 men had to finish the remaining work without the additional men, they would have taken:
\[ \text{Total days} = 35 \text{ days} + 10 \text{ days} = 45 \text{ days} \]

8. **Determine how many days behind schedule it would have been:**
Since they would have completed the work in 45 days, and the builder had originally planned for 45 days, there would be no delay. However, if we consider the scenario where the additional men were not employed, they would have taken:
\[ \text{Total days without additional men} = 35 + 10 = 45 \text{ days} \]
Thus, they would finish exactly on time.

### Conclusion:
If the builder had not employed the additional 53 men, he would have finished the construction in **50 days**, which means he would be **5 days behind schedule**.