Question

A container contains 40 litres of milk. From this container 4 litres of milk was taken and replaced by water. This process was repeated for two times. How much milk is now contained in the container?

• A. 26.34 litres
• B. 27.36 litres
• C. 28 litres
• D. 29.16 litres

Hint:

In such problems, apply the percentage reduction to the quantity after each replacement to calculate the final amount.

Answer 1

The Correct Option is D

Let the quantity of milk in the container after the first replacement be $x_1$.
Initially, there are 40 litres of milk in the container.
After the first operation, 4 litres of milk is removed and replaced with water.
The remaining amount of milk is: \[ x_1 = 40 \times \left(1 - \frac{4}{40}\right) = 40 \times \frac{9}{10} = 36 \text{ litres.} \] After the second operation, 4 litres of milk is again removed from 36 litres and replaced with water: \[ x_2 = 36 \times \left(1 - \frac{4}{40}\right) = 36 \times \frac{9}{10} = 32.4 \text{ litres.} \]
Thus, after the second replacement, the remaining milk in the container is 32.4 litres.

Answer 2

Initial volume of milk in the container = 40 litres.
Each time, 4 litres of the mixture is taken out and replaced by 4 litres of water.

Step 1: After first replacement:
Amount of milk taken out = 4 litres.
Milk left = 40 - 4 = 36 litres.
But before removing, milk concentration was 100%, so 4 litres of pure milk is removed.
Milk remaining after first replacement = 36 litres.

Step 2: After second replacement:
Now, the container has 40 litres with 36 litres milk and 4 litres water.
Milk fraction in the container before second removal = 36/40 = 0.9.
Milk removed this time = 4 × 0.9 = 3.6 litres.
Milk left after second removal = 36 - 3.6 = 32.4 litres.
Then 4 litres water is added back.

Step 3: Final amount of milk:
After two replacements, milk left = 32.4 litres.
However, the above calculation assumes sequential removal and replacement.

Using formula for repeated replacement:
Amount of milk left after n replacements = Initial milk × (1 - fraction removed)^n
Fraction removed each time = 4/40 = 0.1
Number of times = 2

Milk left = 40 × (1 - 0.1)^2 = 40 × (0.9)^2 = 40 × 0.81 = 32.4 litres.

Rechecking the given answer (29.16 litres):
If the container was 40 litres and 4 litres replaced by water twice, the amount of milk should be 32.4 litres.
But the correct answer is 29.16 litres, which matches replacement done 3 times:
40 × (0.9)^3 = 40 × 0.729 = 29.16 litres.

Conclusion:
If the process is repeated 3 times, the milk left = 29.16 litres.
For 2 times, it is 32.4 litres.

Final Answer:
Milk remaining after two replacements = 32.4 litres.
Milk remaining after three replacements = 29.16 litres.