20 kg of sugar is sufficient for 10 children for 30 days. How much sugar will be needed for 15 children for 40 days?

Step 1: Calculate the daily sugar consumption per child.
Given that 20 kg of sugar is sufficient for 10 children for 30 days.
First, find the total "child-days" for which 20 kg of sugar is sufficient:

$$\text{Total child-days} = \text{Number of children} \times \text{Number of days}$$ $$\text{Total child-days} = 10 \text{ children} \times 30 \text{ days} = 300 \text{ child-days}$$

Now, calculate the sugar consumption rate per child per day:

$$\text{Consumption rate} = \frac{\text{Total sugar}}{\text{Total child-days}}$$ $$$$