A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?a)26.34 litresb)27.36 litresc)28 litresd)29.16 litresCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Problem:
A container initially contains 40 litres of milk. From this container, 4 litres of milk is taken out and replaced by water. This process is repeated two more times. We need to determine the amount of milk that is now contained by the container.

Solution:
To solve this problem, we need to understand the concept of successive dilutions and the resulting final concentration.

Initial Concentration:
The container initially contains 40 litres of milk. Therefore, the initial concentration of milk in the container is 100%.

First Dilution:
In the first dilution, 4 litres of milk is taken out and replaced by water. Since 4 litres of milk is removed from the container, the remaining amount of milk is 40 - 4 = 36 litres. However, this 36 litres of milk is now diluted in a total volume of 40 litres (36 litres of milk + 4 litres of water). Therefore, the concentration of milk after the first dilution is:

(36/40) * 100% = 90%

Second Dilution:
In the second dilution, 4 litres of milk is again taken out and replaced by water. Similar to the first dilution, the remaining amount of milk is diluted in a total volume of 40 litres. The remaining amount of milk after the first dilution was 36 litres, so after the second dilution, the amount of milk is:

(36/40) * 100% = 90%

Third Dilution:
In the third dilution, 4 litres of milk is once again taken out and replaced by water. The remaining amount of milk after the second dilution was 36 litres, so after the third dilution, the amount of milk is:

(36/40) * 100% = 90%

Final Concentration:
Since the concentration of milk remains the same after each dilution, the final concentration of milk in the container is 90%.

Calculating the Amount of Milk:
To calculate the amount of milk in the container, we need to determine what 90% of 40 litres is:

(90/100) * 40 = 36 litres

Therefore, the container now contains 36 litres of milk.

Therefore, the correct answer is option 'D' - 29.16 litres.

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