The ratio of milk and water in a mixture is $3:7$. If we add $10\text{ litres}$ of water to the mixture, then the ratio becomes $1:3$. Find the initial quantity of milk.

Step 1: Let the initial quantity of milk and water be $3x$ and $7x$ respectively.
Step 2: According to the problem, $10\text{ litres}$ of water is added to the mixture, making the new ratio $1:3$.

$$\frac{3x}{7x+10}=\frac{1}{3}$$

Step 3: Cross-multiply to solve for $x$:

$$3\times 3x=1\times (7x+10)$$

$$9x=7x+10$$

$$9x-7x=10$$

$$2x=10$$

$$x=5$$

Step 4: Find the initial quantity of milk.

$$\text{Initial quantity of milk}=3x=3\times 5=15\text{ litres}$$