1. **Problem statement:** We are given that the stay of 12 men for 7 days costs 21200. We need to find the cost for the stay of 10 men for 8 days. 2. **Formula and concept:** The cost is directly proportional to the number of men and the number of days. So, we use the formula: $$\text{Cost} \propto \text{Number of men} \times \text{Number of days}$$ 3. **Calculate the cost per man per day:** $$\text{Cost per man per day} = \frac{21200}{12 \times 7} = \frac{21200}{84} = 252.38$$ 4. **Calculate the cost for 10 men for 8 days:** $$\text{Cost} = 252.38 \times 10 \times 8 = 20190.48$$ 5. **Final answer:** The cost for the stay of 10 men for 8 days is approximately 20190.48.