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According to the problem given, they mentioned to us that in the initial stage there was only milk and the quantity of milk is $82litres$.

Later on, as per data one-third of the total milk is removed and the same amount of water is added.

So, firstly we should find the value of one-third in the $82litres$.

It can be simply found by dividing the value with the three.

So,

One-third of the milk $ = \dfrac{1}{3} \times 82= 27.33liters$

And one more thing we need to remember is that in the question itself it mentioned that the same amount of water is added to the milk again.

So, the total quantity will not change at all.

Now, the mixture contains $82litres$ in which $27.33liters$ is water and rest is milk.

So, in order to find out the milk quantity simply we should remove the water quantity from the total mixture quantity.

Hence, milk quantity $ = 82 - 27.33 = 54.67liters$

Up to now, everything is perfect. Now it is mentioned in the given data that again one-third of the present mixture is replaced with the same amount of water. So, as the total quantity of mixture is $82litres$, its one- third quantity is $27.33liters$ as we have already calculated before.

But, in this case this $27.33liters$ of taken out mixture contains both milk and water.

And they will be also in the one-third proportions with their respective quantities.

So, one-third in the $54.67liters$ of milk is $ = \dfrac{1}{3} \times 54.67$

$ = 18.22liters$

After removal of $18.22liters$ milk, remaining milk $ = 54.67 - 18.22$

$ = 36.45liters$

Similarly, we can find water too.

So, one-third in the $27.33liters$ of water is $ = \dfrac{1}{3} \times 27.33= 9.11liters$

After removal of $9.11liters$ water, remaining water $ = 27.33 - 9.11$

$ = 18.22liters$

Now, we got both the quantities values of milk and water.

Milk and water are $36.45liters$ and $18.22liters$ respectively in the mixture.

Ratio of milk and water in the mixture $ = \dfrac{{36.45}}{{18.22}}$

$ \approx 2$

Hence, we can conclude that the ratio of milk and water in the mixture is $2:1$.