Answer :
To solve the problem of determining the current ratio of milk and water in a mixture, we need to go through the following steps:
Initial Composition:
- The mixture initially consists of 42.75 L with milk and water in a ratio of 11:6.
- Let the amounts of milk and water be [tex]11x[/tex] and [tex]6x[/tex] respectively.
- The total parts = 11 + 6 = 17.
- Thus, [tex]11x + 6x = 42.75[/tex]. Solving for [tex]x[/tex], we find [tex]x = \frac{42.75}{17} = 2.5[/tex].
- Therefore, the initial amount of milk is [tex]11 \times 2.5 = 27.5[/tex] L and water is [tex]6 \times 2.5 = 15[/tex] L.
First Adjustment:
- 15 L of the mixture is removed.
- Since the ratio was 11:6, the amount of milk in 15 L = [tex]\frac{11}{17} \times 15 = 9.7059[/tex] L (approximately 9.71 L), and the amount of water = [tex]\frac{6}{17} \times 15 = 5.2941[/tex] L (approximately 5.29 L).
- The new amounts after removal are: milk = [tex]27.5 - 9.71 = 17.79[/tex] L, and water = [tex]15 - 5.29 = 9.71[/tex] L.
- We add 20 L of water, so total water = [tex]9.71 + 20 = 29.71[/tex] L.
Second Adjustment:
- 10 L of the new mixture is removed.
- The new ratio is milk to water, which can be calculated from the current numbers.
- Let's assume parts of milk and water are removed based on their proportions. Remaining milk = [tex]\frac{17.79}{47.5} \times 10[/tex] = 3.75 L (approximately), and water = [tex]\frac{29.71}{47.5} \times 10 = 6.25[/tex].
- The new amounts after this removal are: milk = [tex]17.79 - 3.75 = 14.04[/tex] L, and water = [tex]29.71 - 6.25[/tex] L.
- Add 40 L of water, water = [tex]23.46 + 40 = 63.46[/tex] L.
Final Ratio:
- The final amounts are 14.04 L of milk and 63.46 L of water.
- To get the ratio, divide both by their greatest common divisor. The calculation gives approximately:
[tex]\text{Ratio of milk to water} = \frac{14.04}{63.46}\approx 21:47[/tex]
Answer:
- The current ratio of milk to water is [tex]21:47[/tex].
The correct answer is option (a) 21 : 47.
