A constrator employed 210 men to build a house in 60 days. After 12 days.he was joined by 70 more men. In how many days will the remaining work be finished?
Hint. 210 men can complete the remaning work in 48 days.Find in how many days 280 men can do it.

Answer

To solve the problem step by step, we will follow the hints provided and use the unitary method.

### Step 1: Calculate the total work done by 210 men in 12 days.
- **Total work** can be represented in terms of man-days.
- If 210 men can complete the work in 60 days, the total work is:
\[ \text{Total Work} = 210 \text{ men} \times 60 \text{ days} = 12600 \text{ man-days} \]

### Step 2: Calculate the work done in the first 12 days.
- In 12 days, the work done by 210 men is:
\[ \text{Work done in 12 days} = 210 \text{ men} \times 12 \text{ days} = 2520 \text{ man-days} \]

### Step 3: Calculate the remaining work.
- The remaining work after 12 days is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done in 12 days} \]
\[ \text{Remaining Work} = 12600 \text{ man-days} - 2520 \text{ man-days} = 10080 \text{ man-days} \]

### Step 4: Determine the new workforce.
- After 12 days, 70 more men join the original 210 men, making the total number of men:
\[ \text{Total Men} = 210 + 70 = 280 \text{ men} \]

### Step 5: Calculate the time taken by 280 men to complete the remaining work.
- If 280 men are working, we need to find out how many days it will take to complete 10080 man-days of work:
\[ \text{Days} = \frac{\text{Remaining Work}}{\text{Total Men}} = \frac{10080 \text{ man-days}}{280 \text{ men}} = 36 \text{ days} \]

### Final Answer:
The remaining work will be finished in **36 days**.

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