A mixture has milk and water in the ratio (by volume) of 8 : 3. If 3 litres of water is added to it, then new ratio of milk and water becomes 2 : 1. What are the quantities of milk and water respectively in the mixture initially?

Initially mixture  is 8:3 

After adding 3 lit water it becomes 2:1 

It means quantity of milk is remain unchanged and water is changed in mixture 

2:1 $$\times 4$$ (to equal the milk quantity )

= 8:4

Now milk ratio is same and water is changed after adding water 

the difference in the ratio (8:3)-(8:4) is 0: 1

1unit -> 3 lit 

Given that intial mix. Ratio =8:3

 Milk =$$ 8\times 3 $$= 24 litre

Water = $$ 3\times 3 $$= 9 litre