Mixtures And Allegations

To solve this problem, we will follow the process of dilution and calculate the final concentration of mango juice after repeated removal and replacement with water.

Initially, let the volume of the container be (we can assume any unit since the ratio is dimensionless).

Initially, the entire volume is mango juice.

Step 1: One-fifth of the juice is taken out and replaced by water. Hence, the juice left in the container is:

Step 2: Repeat the process:

Step 3: Repeat the process again:

Step 4: Repeat the process one more time:

Substitute the value of , thus:

Since the container is now filled with juice and water, the amount of water is:

Hence, the final ratio of juice to water is:

Therefore, the final ratio of juice and water in the container is: .

Step 1: Understanding the Concept:
This is a problem of mixtures where a certain quantity of the original substance is removed and replaced with another substance repeatedly. The key is to calculate the fraction of the original substance that remains after each operation.
Step 2: Key Formula or Approach:
The formula for calculating the final quantity of the original substance after 'n' successive replacements is: Where 'n' is the number of times the operation is performed.
Step 3: Detailed Explanation:
Let's identify the given values:
Initial Quantity of milk = 60 litres.
Total Volume of the mixture = 60 litres (this remains constant).
Quantity Replaced in each step = 6 litres.
The process was performed once, and then "repeated further two more times". So, the total number of operations is .
Now, we apply the formula: First, simplify the fraction inside the parenthesis: So the expression becomes: Calculate : Finally, multiply this by the initial quantity: Step 4: Final Answer:
After three operations, the amount of milk remaining in the tub is 43.74 litres.

Step 1: Understanding the Concept:
This is a problem of mixtures where a certain quantity of the original substance is removed and replaced with another substance repeatedly. The key is to calculate the fraction of the original substance that remains after each operation.
Step 2: Key Formula or Approach:
The formula for calculating the final quantity of the original substance after 'n' successive replacements is: Where 'n' is the number of times the operation is performed.
Step 3: Detailed Explanation:
Let's identify the given values:
Initial Quantity of milk = 60 litres.
Total Volume of the mixture = 60 litres (this remains constant).
Quantity Replaced in each step = 6 litres.
The process was performed once, and then "repeated further two more times". So, the total number of operations is .
Now, we apply the formula: First, simplify the fraction inside the parenthesis: So the expression becomes: Calculate : Finally, multiply this by the initial quantity: Step 4: Final Answer:
After three operations, the amount of milk remaining in the tub is 43.74 litres.