The ratio of milk and water in a pot is $3:4$. If we add $10\text{ litres}$ milk and $10\text{ litres}$ water, then the ratio becomes $4:5$. How much quantity of total mixture was present initially?

Let the initial quantities of milk and water be $3x$ and $4x$ respectively.
$$\text{Total initial mixture}=3x+4x=7x$$

According to the problem, $10\text{ litres}$ of milk and $10\text{ litres}$ of water are added, resulting in a new ratio of $4:5$:

$$\frac{3x+10}{4x+10}=\frac{4}{5}$$

Cross-multiply to solve for $x$:

$$5(3x+10)=4(4x+10)$$

$$15x+50=16x+40$$

$$16x-15x=50-40⟹x=10$$

Now, substitute the value of $x$ back to find the initial total mixture:

$$\text{Total initial mixture}=7x=7\times 10=70\text{ litres}$$