'X', 'Y', and 'Z' are three mixtures of milk and water. The ratio of quantity of milk to that of water in mixtures 'X', 'Y', and 'Z' is 4:5, 2:3, and 3:4, respectively. If mixtures 'X', 'Y', and 'Z' are mixed in the ratio 3:5:2, find the concentration of milk in the final mixture.

Let the quantities of mixtures 'X', 'Y', and 'Z' in the final mixture be 3a, 5a, and 2a, respectively. Now, calculate the amount of milk in each mixture: Milk in 'X' = (4/9) × 3a = (12a/9) = (4a/3) Milk in 'Y' = (2/5) × 5a = (10a/5) = 2a Milk in 'Z' = (3/7) × 2a = (6a/7) Total amount of milk = (4a/3) + 2a + (6a/7) LCM of 3 and 7 = 21, so: (4a/3) = (28a/21), (2a) = (42a/21), (6a/7) = (18a/21) Total amount of milk = (28a + 42a + 18a) / 21 = (88a/21) Now, calculate the total quantity of the final mixture: Total mixture = 3a + 5a + 2a = 10a The concentration of milk = (Total amount of milk / Total mixture) × 100 = (88a/21) / 10a × 100 = (88/210) × 100 = 41.90% ≈ 42% Correct option: b