18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of 2 : 1. If the resultant respective ratio of milk and water in the vessel was 4 : 1, what was the quantity of pure milk added in the vessel ? (in litres)

18 litres of pure water was added to a vessel containing 80 litres of pure milk. 

Total mixture = 80 + 18 = 98 litres

Now, 49 litres i.e., $$\frac{1}{2}$$is removed, => Milk left = $$\frac{80}{2}$$ = 40 litres

Water left = $$\frac{18}{2}$$ = 9 litres

Let milk added be $$2x$$ litres and water added is $$x$$ litres

=> $$\frac{40 + 2x}{9 + x} = \frac{4}{1}$$

=> $$40 + 2x = 36 + 4x$$

=> $$2x = 40 - 36 = 4$$

=> $$x = \frac{4}{2} = 2$$

$$\therefore$$ Quantity of milk added = $$2 \times 2 = 4$$ litres