1. **Problem statement:** A contractor employs 20 men to finish a project in 50 days. After 15 days, 10 men leave, and the remaining 10 men increase their working hours from 6 hours/day to 9 hours/day. We need to find the total number of days to complete the project. 2. **Formula and concepts:** Work done = Number of men \( \times \) Hours per day \( \times \) Number of days. 3. **Step 1: Calculate total work in man-hours.** \[ \text{Total work} = 20 \times 6 \times 50 = 6000 \text{ man-hours} \] 4. **Step 2: Calculate work done in the first 15 days.** \[ \text{Work done} = 20 \times 6 \times 15 = 1800 \text{ man-hours} \] 5. **Step 3: Calculate remaining work.** \[ \text{Remaining work} = 6000 - 1800 = 4200 \text{ man-hours} \] 6. **Step 4: Calculate daily work after 15 days with 10 men working 9 hours/day.** \[ \text{Daily work} = 10 \times 9 = 90 \text{ man-hours/day} \] 7. **Step 5: Calculate days needed to finish remaining work.** \[ \text{Days} = \frac{4200}{90} = 46.67 \text{ days} \] 8. **Step 6: Calculate total days to complete the project.** \[ \text{Total days} = 15 + 46.67 = 61.67 \approx 62 \text{ days} \] **Answer:** The project is completed in approximately 62 days.