In 80 litres pure milk, 8 litres of milk is replaced by water if this process…

Given: Initial quantity of pure milk = 80 litres. Each time 8 litres of mixture is removed and replaced by water. The process is repeated two times.

Idea: When x litres are removed from a total of V litres, the fraction of milk remaining after one replacement is (1 - x/V). Repeating the process n times multiplies this fraction n times.

1. Fraction of milk remaining after one replacement = 1 - 8/80 = 1 - 0.1 = 0.9 = 9/10.

2. After two repetitions the fraction = (9/10)^2 = 81/100.

3. Amount of milk = 80 × 81/100 = 64.8 litres.

4. Amount of water = 80 - 64.8 = 15.2 litres.

5. Ratio milk:water = 64.8 : 15.2 = (64.8 ÷ 0.8) : (15.2 ÷ 0.8) = 81 : 19.

Answer: 81 : 19