1. **State the problem:** We have a piece of work done by 8 men working 10 hours a day in 15 days. We want to find how many hours per day 12 men must work to complete the same work in 10 days. 2. **Formula and concept:** The total work done can be expressed as the product of the number of men, hours per day, and number of days. Total work = number of men \times hours per day \times number of days 3. **Calculate total work done by the first group:** $$\text{Work} = 8 \times 10 \times 15 = 1200$$ 4. **Set up equation for the second group:** Let $h$ be the hours per day 12 men must work to complete the work in 10 days. $$12 \times h \times 10 = 1200$$ 5. **Solve for $h$:** $$120h = 1200$$ $$h = \frac{1200}{120}$$ $$h = 10$$ 6. **Interpretation:** 12 men must work 10 hours per day to complete the work in 10 days.