15 men can complete a work in 12 days they start the work together . In how many days the total work will be finished when.
After 4 days 5 men left the work .

Answer

To solve the problem step by step, we will first determine the total amount of work and then calculate how the work progresses over the days with the changes in the number of workers.

### Step 1: Calculate the Total Work
Given that 15 men can complete the work in 12 days, we can calculate the total work in terms of "man-days".

Total work = Number of men × Number of days
Total work = 15 men × 12 days = 180 man-days

### Step 2: Work Done in the First 4 Days
Next, we need to find out how much work is completed in the first 4 days by the 15 men.

Work done in 4 days = Number of men × Number of days
Work done in 4 days = 15 men × 4 days = 60 man-days

### Step 3: Calculate Remaining Work
Now, we can find the remaining work after the first 4 days.

Remaining work = Total work - Work done in 4 days
Remaining work = 180 man-days - 60 man-days = 120 man-days

### Step 4: Determine the New Number of Workers
After 4 days, 5 men leave the work, so the number of men left is:

Number of men left = 15 men - 5 men = 10 men

### Step 5: Calculate Days Required to Finish Remaining Work
Now we need to find out how many days it will take for the remaining 10 men to finish the remaining work of 120 man-days.

Days required = Remaining work / Number of men
Days required = 120 man-days / 10 men = 12 days

### Step 6: Calculate Total Days to Complete the Work
Finally, we add the 4 days worked initially to the 12 days required to finish the remaining work.

Total days = Days worked initially + Days required to finish remaining work
Total days = 4 days + 12 days = 16 days

### Conclusion
The total work will be finished in **16 days**.

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