A mixture contains alcohol and water in ratio $4:5$. If $10\text{litres}$ of water is added to $27\text{litres}$ of the mixture, find the new ratio of alcohol to water.

1. Determine the initial components in $27\text{litres}$ of the mixture:
* Sum of the ratio components = $4+5=9$
* Volume of Alcohol = $\frac{4}{9}\times 27=12\text{litres}$
* Volume of Water = $\frac{5}{9}\times 27=15\text{litres}$

2. New quantities after adding $10\text{litres}$ of water:

* Alcohol remains unchanged = $12\text{litres}$
* New Volume of Water = $15+10=25\text{litres}$

3. Calculate the new ratio:

$$\text{New Ratio}=\frac{\text{Alcohol}}{\text{Water}}=\frac{12}{25}=12:25$$