To determine the new ratio of milk and water, let's consider the initial ratio and the changes made to the mixture.
### Initial Mixture:
- Total volume of the mixture: 40 liters
- Ratio of milk to water: 5:3
From the given ratio 5:3:
- The fraction of milk in the mixture is [tex]\( \frac{5}{5+3} = \frac{5}{8} \)[/tex]
- The fraction of water in the mixture is [tex]\( \frac{3}{5+3} = \frac{3}{8} \)[/tex]
Calculating the initial volumes:
- Initial volume of milk: [tex]\( 40 \times \frac{5}{8} = 25 \)[/tex] liters
- Initial volume of water: [tex]\( 40 \times \frac{3}{8} = 15 \)[/tex] liters
### After Removing 8 Liters of Mixture:
When 8 liters of the mixture (containing milk and water in the same 5:3 ratio) is removed:
- Volume of milk removed: [tex]\( 8 \times \frac{5}{8} = 5 \)[/tex] liters
- Volume of water removed: [tex]\( 8 \times \frac{3}{8} = 3 \)[/tex] liters
Volumes after removal:
- Volume of milk remaining: [tex]\( 25 - 5 = 20 \)[/tex] liters
- Volume of water remaining: [tex]\( 15 - 3 = 12 \)[/tex] liters
### Adding 8 Liters of Water:
The 8 liters removed are replaced by 8 liters of water:
- New volume of milk: 20 liters
- New volume of water: [tex]\( 12 + 8 = 20 \)[/tex] liters
### New Ratio:
The final volumes in the mixture are:
- Milk: 20 liters
- Water: 20 liters
The new ratio of milk to water is [tex]\( 20:20 \)[/tex].
Simplifying this ratio:
- [tex]\( \frac{20}{20} = 1 \)[/tex]
- This gives the ratio [tex]\( 1:1 \)[/tex]
Therefore, the ratio of milk and water in the resultant mixture is [tex]\( \boxed{1:1} \)[/tex].
So, the correct answer is:
D) [tex]\( 1:1 \)[/tex]
