From a container having pure milk, 40% is replaced by water and the process is repeated thrice. At the end of the third operation, the purity of milk is:

Let the initial purity (or quantity) of pure milk be 100%.
In each operation, 40% of the content is removed and replaced with water. This means 100%−40%=60% of the milk remains after each step.

The process is repeated thrice (a total of 3 operations).
The remaining concentration of milk can be calculated using the formula:

Final Concentration=Initial Concentration×(1−
V
x
​
)
n

Where:

Initial Concentration = 100%

Fraction removed
V
x
​
=40%=0.4

Number of repetitions n=3

Final Purity=100×(1−0.4)
3

Final Purity=100×(0.6)
3

Final Purity=100×0.216=21.60%
Thus, at the end of the third operation, the purity of milk is 21.60%.