In a $2025\text{ litre}$ mixture of milk and water, the ratio of milk to water is $12:13$. To get a new mixture containing milk and water in the ratio of $12:15$, the amount of water to be added is:

Initial ratio of Milk : Water = $12:13$.
Total parts initially = $12+13=25$ units.
Given total volume = $2025\text{ litres}$.

$$\text{Value of 1 unit}=\frac{2025}{25}=81\text{ litres}$$

The final desired ratio is $12:15$.
Notice that the milk part remains unchanged ($12$ units), while the water part increases from $13$ to $15$ units.

$$\text{Increase in water}=15-13=2\text{ units}$$

Amount of water to be added:

$$\text{Water to add}=2\times 81=162\text{ litres}$$