Question

A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

• A. 29.16 litre
• B. 43.74 litre
• C. 42.24 litre
• D. 38.74 litre

Hint:

In mixture replacement problems, focus on the fraction of the original liquid that remains after one operation. In this case, \(1 - 6/60 = 9/10\) of the milk remains. For three operations, you simply calculate \( \text{Initial} \times (\frac{9}{10}) \times (\frac{9}{10}) \times (\frac{9}{10}) \).

Answer 1

The Correct Option is B

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: \[ \text{Final Quantity} = \text{Initial Quantity} \times \left(1 - \frac{\text{Quantity Replaced}}{\text{Total Volume}}\right)^n \] 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 \(n = 1 + 2 = 3\).
Now, we apply the formula: \[ \text{Amount of milk left} = 60 \times \left(1 - \frac{6}{60}\right)^3 \] First, simplify the fraction inside the parenthesis: \[ \frac{6}{60} = \frac{1}{10} = 0.1 \] So the expression becomes: \[ \text{Amount of milk left} = 60 \times (1 - 0.1)^3 \] \[ = 60 \times (0.9)^3 \] Calculate \( (0.9)^3 \): \[ (0.9)^3 = 0.9 \times 0.9 \times 0.9 = 0.81 \times 0.9 = 0.729 \] Finally, multiply this by the initial quantity: \[ \text{Amount of milk left} = 60 \times 0.729 \] \[ = 43.74 \] Step 4: Final Answer:
After three operations, the amount of milk remaining in the tub is 43.74 litres.