1. **Problem statement:** We need to find how long 15 chickens and 4 ducks will take to eat 10 kg of grain, given that 10 chickens eat a 6 kg sack in 24 hours and 10 chickens eat in the same time as 8 ducks. 2. **Given:** - 10 chickens eat 6 kg in 24 hours. - Time taken by 10 chickens = Time taken by 8 ducks. 3. **Find:** Time taken by 15 chickens and 4 ducks to eat 10 kg. 4. **Step 1: Calculate the rate of 1 chicken.** - Total grain eaten by 10 chickens in 24 hours = 6 kg. - Rate of 10 chickens = $\frac{6}{24} = 0.25$ kg/hour. - Rate of 1 chicken = $\frac{0.25}{10} = 0.025$ kg/hour. 5. **Step 2: Calculate the rate of 1 duck.** - Since 10 chickens eat in the same time as 8 ducks, their rates are equal: $$10 \times \text{rate of chicken} = 8 \times \text{rate of duck}$$ - Substitute rate of chicken: $$10 \times 0.025 = 8 \times \text{rate of duck}$$ - Solve for rate of duck: $$\text{rate of duck} = \frac{10 \times 0.025}{8} = \frac{0.25}{8} = 0.03125 \text{ kg/hour}$$ 6. **Step 3: Calculate combined rate of 15 chickens and 4 ducks.** - Rate of 15 chickens = $15 \times 0.025 = 0.375$ kg/hour. - Rate of 4 ducks = $4 \times 0.03125 = 0.125$ kg/hour. - Combined rate = $0.375 + 0.125 = 0.5$ kg/hour. 7. **Step 4: Calculate time to eat 10 kg at combined rate.** - Time = $\frac{\text{Total grain}}{\text{Combined rate}} = \frac{10}{0.5} = 20$ hours. **Final answer:** It will take 15 chickens and 4 ducks 20 hours to eat 10 kg of grain.