Given:
- The mixture contains 40 liters of milk and water.
- The mixture has 10% water.
- We need to find out how much water should be added to the mixture so that the new mixture contains 20% water.

Let's solve this problem step by step:

Step 1: Finding the amount of water in the initial mixture
- The initial mixture contains 10% water.
- So, the amount of water in the initial mixture = 10% of 40 liters = (10/100) * 40 = 4 liters

Step 2: Finding the amount of milk in the initial mixture
- Since the initial mixture contains 40 liters of milk and water, the amount of milk in the initial mixture can be calculated by subtracting the amount of water from the total mixture.
- Amount of milk = Total mixture - Amount of water
- Amount of milk = 40 liters - 4 liters = 36 liters

Step 3: Adding water to the mixture
- Let's assume we add 'x' liters of water to the initial mixture.
- After adding 'x' liters of water, the total amount of water in the mixture becomes 4 + x liters.
- The total amount of mixture after adding water will be 40 + x liters.

Step 4: Finding the percentage of water in the new mixture
- The new mixture should contain 20% water.
- So, the amount of water in the new mixture should be 20% of the total mixture.
- Amount of water in the new mixture = 20% of (40 + x) liters = (20/100) * (40 + x) = (2/10) * (40 + x) = (2/10) * 40 + (2/10) * x = 8 + 0.2x liters

Step 5: Equating the amount of water in the new mixture
- According to the problem, the amount of water in the new mixture should be equal to the amount of water in the initial mixture.
- 8 + 0.2x = 4

Step 6: Solving the equation for 'x'
- 0.2x = 4 - 8
- 0.2x = -4
- x = -4 / 0.2
- x = -20

Since the amount of water cannot be negative, we can conclude that no water should be added to the initial mixture in order to obtain a new mixture with 20% water.

Therefore, the correct answer is option 'd) None of the above'.