A 180 litre mixture contains 80% milk and the rest water. At first, 30 litres of the mixture are removed and replaced with 10 litres of water. Then 40 litres of the resultant mixture are removed and replaced with 'x' litres of milk such that the ratio of the quantity of milk to that of water in the final mixture becomes 19:6, respectively. Find the value of 'x'?

Ratio of quantity of milk to that of water, in the initial mixture = 80:20 = 4:1 After removing 30 litres of the mixture and adding 10 litres of water, quantity of milk in the mixture = (180 − 30) × (4/5) = 120 litres quantity of water in the mixture = (180 − 30) × (1/5) + 10 = 30 + 10 = 40 litres So, ratio of quantity of milk to that of water, now = 120:40 = 3:1 After removing 40 litres of the mixture (in the same 3:1 proportion) and replacing with 'x' litres of milk, quantity of milk removed = 40 × (3/4) = 30 litres quantity of water removed = 40 × (1/4) = 10 litres So, milk left = 120 − 30 = 90 litres; water left = 40 − 10 = 30 litres New quantity of milk = 90 + x litres; water remains = 30 litres ATQ, (90 + x):30 = 19:6 Or, 6 × (90 + x) = 19 × 30 Or, 540 + 6x = 570 Or, 6x = 30 So, x = 5 Hence, the correct answer is A.