$40\text{ litres}$ of a mixture contains milk and water in the ratio of $17:3$. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes $7:1$. The quantity of milk added to it was

Step 1: Find the initial quantities of milk and water.
Total volume of mixture = $40\text{ litres}$
Initial ratio of Milk $:$ Water = $17:3$
Sum of ratio terms = $17+3=20$

$$\text{Initial Milk}=\frac{17}{20}\times 40=34\text{ litres}$$

$$\text{Initial Water}=\frac{3}{20}\times 40=6\text{ litres}$$

Step 2: Set up the equation for the new mixture.
Let the quantity of milk added be $x\text{ litres}$.
The new quantity of milk becomes $(34+x)\text{ litres}$, while the quantity of water remains unchanged at $6\text{ litres}$.

The new ratio is given as $7:1$.

$$\frac{34+x}{6}=\frac{7}{1}$$

**Step 3: Solve for $x$.**

$$34+x=7\times 6$$

$$34+x=42$$

$$x=42-34$$

$$x=8\text{ litres}$$

Therefore, the quantity of milk added was $8\text{ litres}$.