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In the question it is given that,

Quantity of the mixture is 60 liters

The ratio of milk and water in that mixture is 2:1

Hence, the quantity of milk in the mixture is $\left( {60 \times \dfrac{2}{3}} \right) = 40 litres$

And the quantity of water in the mixture is $60 - 40 = 20 litres$

The needed new ratio of milk and water is 1:2

In the question it is asked to add water in the mixture that means the quantity of milk will remain the same.

Let the quantity of water to be added further is x litres

Then the ratio of milk and water will be $\dfrac{{40}}{{20 + x}}$

According to question, the ratio is $\dfrac{{1}}{{2}}$

Hence, $\dfrac{{40}}{{20 + x}} = \dfrac{1}{2}$

By cross multiplication we get,

$80 = 20 + x$

$ \Rightarrow x = 80 - 20 = 60 litres$

Hence the quantity of water to be added is 60 litres.

Alternative method- In the question it is given that,

Quantity of the mixture is 60 litres

The ratio of milk and water in that mixture is 2:1

Hence, the quantity of milk in the mixture is $\left( {60 \times \dfrac{2}{3}} \right) = 40 litres$

And the quantity of water in the mixture is $60 - 40 = 20 litres$

The needed new ratio of milk and water is 1:2

Let in the new mixture, quantity of milk be x and quantity of water be 2x

In the question it is asked to add water in the mixture that means the quantity of milk will remain the same.

Hence, $x = 40$ litres

Then, quantity of water, $2x = 80$ litres

Quantity of water needed to be added is $80 - 20 = 60 litres$.