A mixture contains 50% water and rest milk. 30 litres from the mixture is replaced with same quantity of milk. If the ratio of quantity of milk to that of water in the resultant mixture is 7:4, then find the initial quantity of the mixture.

Since, the 30 litres is withdrawn from the total mixture, it won't affect the ratio of milk to water in the mixture. Let the initial quantity of water in the mixture after withdrawing 30 litres be '4x' litres So, total quantity of mixture after withdrawing 30 litres = 4x ÷ 0.5 = '8x' litres And quantity of milk in the mixture after withdrawing 30 litres = 8x - 4x = '4x' litres ATQ; {(4x + 30)/4x} = (7/4) Or, 4x + 30 = 7x So, x = 10 So, total quantity of mixture after withdrawing 30 litres = 8 × 10 = 80 litres So, initial quantity of mixture = 80 + 30 = 110 litres