60 men can complete a work in 30 days. They started the work together, but at the end of each 10th day, 10 men left the job. The work was completed in how many days?

Options

A. 36
B. 30
C. 40
D. 45

Answer

To solve the problem step by step, we will determine how many days it takes for the work to be completed given the conditions stated in the question.

### Step 1: Calculate the total work in units
We know that 60 men can complete the work in 30 days.

- Total work = Number of men × Number of days
- Total work = 60 men × 30 days = 1800 man-days

### Step 2: Work done in the first 10 days
In the first 10 days, all 60 men are working.

- Work done in the first 10 days = Number of men × Number of days
- Work done = 60 men × 10 days = 600 units

### Step 3: Calculate remaining work after the first 10 days
After the first 10 days, the remaining work is:

- Remaining work = Total work - Work done in the first 10 days
- Remaining work = 1800 units - 600 units = 1200 units

### Step 4: Work done in the next 10 days with 50 men
After the first 10 days, 10 men leave, so now 50 men are working.

- Work done in the next 10 days = 50 men × 10 days = 500 units

### Step 5: Calculate remaining work after the second 10 days
After the second 10 days, the remaining work is:

- Remaining work = Remaining work - Work done in the second 10 days
- Remaining work = 1200 units - 500 units = 700 units

### Step 6: Work done in the next 10 days with 40 men
Another 10 men leave, so now 40 men are working.

- Work done in the next 10 days = 40 men × 10 days = 400 units

### Step 7: Calculate remaining work after the third 10 days
After the third 10 days, the remaining work is:

- Remaining work = Remaining work - Work done in the third 10 days
- Remaining work = 700 units - 400 units = 300 units

### Step 8: Work done in the next 10 days with 30 men
Another 10 men leave, so now 30 men are working.

- Work done in the next 10 days = 30 men × 10 days = 300 units

### Step 9: Calculate remaining work after the fourth 10 days
After the fourth 10 days, the remaining work is:

- Remaining work = Remaining work - Work done in the fourth 10 days
- Remaining work = 300 units - 300 units = 0 units

### Step 10: Total days taken to complete the work
Now, we can calculate the total number of days taken:

- Total days = 10 days (first phase) + 10 days (second phase) + 10 days (third phase) + 10 days (fourth phase) = 40 days

Thus, the work was completed in **40 days**.

### Final Answer:
The work was completed in **40 days**.

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