How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

Solution(By Examveda Team)

Total quantity of mixture
$$\eqalign{ & = \frac{7}{{7 + 3}} \times 30{\text{ litres}} \cr & = 21{\text{ litres}} \cr} $$
And quantity of water in the mixture
$$\eqalign{ & = \frac{3}{{7 + 3}} \times 30{\text{ litres}} \cr & = 9{\text{ litres}} \cr} $$
Let water to be mixed 'a' litre
Then,
$$\eqalign{ & \Rightarrow \left( {30 + a} \right) \times \frac{{40}}{{100}} = 9 + a \cr & \Rightarrow 120 + 4a = 90 + 10a \cr & \Rightarrow 120 - 90 = 10a - 4a \cr & \Rightarrow 30 = 6a \cr & \Rightarrow a = 5 \cr} $$
Hence, 5 litres water mixed in the mixture.