We can solve this problem using the concept of "man-hours," which represents the total amount of work done, calculated by multiplying the number of men, the number of hours worked per day, and the number of days worked. The total work done is constant, so we can set up an equation to solve for the unknown number of men needed.

Step 1: Calculate total man-hours required for the first scenario:

In the original setup:

• Number of men = 48
• Number of hours per day = 11
• Number of days = 15

Total man-hours = Number of men × Hours per day × Number of days $\text{Total man-hours} = 48 \times 11 \times 15 = 7920 \text{ man-hours}$

Step 2: Set up the equation for the second scenario:

In the new setup:

• Number of men = $x$ (this is what we need to find)
• Number of hours per day = 10
• Number of days = 12

Total man-hours = $x \times 10 \times 12 = 120x$

Step 3: Set the total man-hours equal for both scenarios:

Since the total work remains the same, we set the total man-hours from both scenarios equal: $7920 = 120x$

Step 4: Solve for $x$:

$x = \frac{7920}{120} = 66$

So, 66 men should be employed to finish the work in 12 days working 10 hours a day.

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Would you like to see any more details on this problem or further clarifications? Here are some related questions you might find interesting:

1. How do man-hours help in determining work schedules?
2. What would happen if we decreased the number of days further (e.g., to 10 days)?
3. How can this concept be used for larger scale projects, like constructing buildings or roads?
4. How do we account for efficiency changes when the number of men changes?
5. What other factors (like worker fatigue) might affect the total man-hours required?

Tip: Always remember that the product of men, hours, and days gives the total work, and if you adjust one of these variables, you can solve for the others while keeping the total work constant!