A container holds 160 litres of pure milk. First, 1/2 of the milk is taken out and replaced with water. Then 3/8 of the resulting mixture is removed and again replaced by water. Find the sum of the terms in the simplified ratio of water to milk in the final mixture.

ATQ, Initially: Milk = 160 litres Water = 0 litres First replacement: 1/2 of milk is replaced with water. Milk removed = 160 × 1/2 = 80 litres Water added = 80 litres After first replacement: Milk = 160 − 80 = 80 litres Water = 80 litres Total mixture = 160 litres Next, 3/8 of the mixture is removed and replaced with water. Mixture removed = 160 × 3/8 = 60 litres At this stage, milk and water are in the ratio 80 : 80 = 1 : 1 So, from 60 litres mixture: Milk removed = 60 × 1/2 = 30 litres Water removed = 60 × 1/2 = 30 litres After removing 60 litres: Milk left = 80 − 30 = 50 litres Water left = 80 − 30 = 50 litres Now, 60 litres water is added again. Final water = 50 + 60 = 110 litres Final milk = 50 litres Final ratio of water to milk = 110 : 50 Simplify by dividing both terms by 10: 110/10 = 11 50/10 = 5 So, simplified ratio of water to milk = 11 : 5 Sum of the terms = 11 + 5 = 16