A mixture contains milk and water in the ratio ______, respectively. 20% of the mixture is taken out and replaced with 40 litres of water such that the ratio of milk to water in the resultant mixture becomes _____. The initial quantity of the mixture is not in between 200 litres and 300 litres.
The values given in which of the following options will fill the blanks in the same order in which it is given to make the statement true:
I. 4:3, 1:1
II. 7:8, 3:7
III. 2:3, 1:2

For I: Let the initial quantity of milk and water in the mixture be 4x litres and 3x litres, respectively.

According to the question,

(0.8 × 4x) / (0.8 × 3x + 40) = 1/1

Or, 3.2x = 2.4x + 40
Or, 0.8x = 40
Or, x = 50

Therefore, total quantity of mixture = 4x + 3x = 7x = 350 litres (possible).

Therefore, I is true. For II: Let the initial quantity of milk and water in the mixture be 7y litres and 8y litres, respectively.

According to the question,

(0.8 × 7y) / (0.8 × 8y + 40) = 3/7

Or, 5.6y = (3/7)(6.4y + 40)
Or, 39.2y = 19.2y + 120
Or, 20y = 120
Or, y = 6

Therefore, total quantity of mixture = 7y + 8y = 15y = 90 litres (possible).

Therefore, II is true. For III: Let the initial quantity of milk and water in the mixture be 2z litres and 3z litres, respectively.

According to the question,

(0.8 × 2z) / (0.8 × 3z + 40) = 1/2

Or, 1.6z = 1.2z + 20
Or, 0.4z = 20
Or, z = 50

Therefore, total quantity of mixture = 2z + 3z = 5z = 250 litres (not possible, as it lies between 200 and 300).

Therefore, III is false. Hence, option B (Only I and II).