A builder decided to build a farmhouse in 45 days. He employed 150 men in the beginning and120 more after 30 days and completed the construction in stipulated time. If he had not employed the additional men, how many days behind schedule would it have been finished?

Answer

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

### Step 1: Calculate the total work done in man-days.
The builder initially employed 150 men for 30 days. The total work done in this period can be calculated as:
\[ \text{Work} = \text{Number of men} \times \text{Number of days} = 150 \times 30 = 4500 \text{ man-days} \]

**Hint:** Remember that man-days represent the total amount of work done, where one man working for one day counts as one man-day.

### Step 2: Determine the remaining work after 30 days.
Since the builder completed the construction in 45 days, he had 15 days left after the first 30 days. The total work required to complete the farmhouse is equal to the work done in the first 30 days plus the work done in the next 15 days with the additional men.

Let’s denote the total work required to complete the farmhouse as \( W \). The work done in the last 15 days with 270 men (150 original + 120 additional) is:
\[ \text{Work} = 270 \times 15 = 4050 \text{ man-days} \]

Thus, the total work \( W \) is:
\[ W = 4500 + 4050 = 8550 \text{ man-days} \]

**Hint:** To find the total work, sum the work done in both phases of construction.

### Step 3: Calculate how long it would take with only 150 men.
If only 150 men were employed for the entire duration, we need to find out how many days it would take to complete 8550 man-days of work:
\[ \text{Days} = \frac{\text{Total Work}}{\text{Number of men}} = \frac{8550}{150} = 57 \text{ days} \]

**Hint:** When calculating the number of days, divide the total work by the number of workers to find out how many days it will take.

### Step 4: Determine how many days behind schedule this would be.
The builder had originally planned to complete the farmhouse in 45 days. If it would take 57 days with only 150 men, we can find how many days behind schedule this is by subtracting the planned days from the actual days taken:
\[ \text{Days behind schedule} = 57 - 45 = 12 \text{ days} \]

**Hint:** To find the delay, simply subtract the scheduled completion time from the actual completion time.

### Final Answer:
The construction would have been finished 12 days behind schedule if the builder had not employed the additional men.

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