20 Men can do a piece of work in 25 days, in how many days will 10 men do it?

Answer

To solve the problem step by step, we can use the concept of work done by men over a period of time. Here’s how we can approach it:

### Step 1: Understand the given information
We know that:
- 20 men can complete the work in 25 days.

### Step 2: Calculate the total work in man-days
To find the total amount of work (in man-days), we can multiply the number of men by the number of days they work:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 20 \text{ men} \times 25 \text{ days} = 500 \text{ man-days} \]

### Step 3: Set up the equation for the second scenario
Now, we need to find out how many days (let's call it \(d_2\)) it will take for 10 men to complete the same amount of work (500 man-days). We can set up the equation:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
So, for 10 men:
\[ 500 \text{ man-days} = 10 \text{ men} \times d_2 \]

### Step 4: Solve for \(d_2\)
Now we can solve for \(d_2\):
\[ d_2 = \frac{500 \text{ man-days}}{10 \text{ men}} = 50 \text{ days} \]

### Conclusion
Thus, 10 men will take 50 days to complete the work.

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