1. **Problem statement:** A group of 25 men can build a bridge in 40 days working 8 hours per day. After working for 20 days, 10 men leave. The remaining men work 9 hours per day. We need to find how many additional days are required to complete the work. 2. **Formula and concept:** Work done = Number of men $ \times $ Number of hours per day $ \times $ Number of days. 3. **Calculate total work in man-hours:** $$\text{Total work} = 25 \times 8 \times 40 = 8000 \text{ man-hours}$$ 4. **Work done in first 20 days:** $$\text{Work done} = 25 \times 8 \times 20 = 4000 \text{ man-hours}$$ 5. **Remaining work:** $$\text{Remaining work} = 8000 - 4000 = 4000 \text{ man-hours}$$ 6. **After 20 days, 10 men leave, so remaining men = 25 - 10 = 15 men. They work 9 hours per day. Let the additional days needed be $d$. 7. **Work done by remaining men in $d$ days:** $$15 \times 9 \times d = 4000$$ 8. **Solve for $d$:** $$d = \frac{4000}{15 \times 9} = \frac{4000}{135} = \frac{\cancel{4000}^{\times 1}}{\cancel{135}^{\times 1}} = 29.63 \text{ days (approximately)}$$ 9. **Final answer:** They will need approximately 29.63 additional days to complete the work.